Updated on 2024/12/21

写真a

 
MIEZAKI, Tsuyoshi
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Degree
Bachelor of Science ( 2004.03 Tokyo University of Science )
Master of Mathematical Sciences ( 2006.03 Kyushu University )
Ph.D. (Mathematical Sciences) ( 2009.03 Kyushu University )
Homepage URL
http://www.f.waseda.jp/miezaki/

Research Experience

  • 2021.04
    -
    Now

    Waseda University

  • 2017.10
    -
    2021.03

    University of the Ryukyus   Faculty of Education

  • 2015.10
    -
    2017.09

    Yamagata University   Faculty of Education, Art and Science

  • 2012.10
    -
    2015.09

    Yamagata University   Faculty of Education, Art and Science

  • 2011.04
    -
    2012.09

    Oita National College of Technology   General Education

  • 2010.04
    -
    2011.03

    Tohoku University   Graduate School of Information Sciences

  • 2009.04
    -
    2010.03

    Hokkaido University   Faculty of Science

  • 2008.04
    -
    2009.03

    Kyushu University   Graduate School of Mathematics Department of Mathematics

▼display all

Education Background

  • 　
    -
    2009.03

    Kyushu University   Graduate School, Division of Mathematical Sciences  

  • 　
    -
    2006.03

    Kyushu University   Graduate School, Division of Mathematical Sciences  

  • 　
    -
    2004.03

    Tokyo University of Science   Faculty of Science  

Research Areas

  • Applied mathematics and statistics   デザイン理論を用いた対称性の探求 / Basic mathematics   デザイン理論を用いた対称性の探求 / Algebra   符号，格子，頂点作用素代数の対称性

Research Interests

  • 代数的組合せ論

Media Coverage

  • 教員免許更新講習

    2013.12

 

Papers

  • Universal graph series, chromatic functions, and their index theory

    Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, Shuhei Tsujie

       2024.12  [Refereed]

    Authorship：Lead author

  • The Tutte polynomials of genus g

    Tsuyoshi Miezaki, Manabu Oura, Tadashi Sakuma, Hidehiro Shinohara

       2024.12  [Refereed]

    Authorship：Lead author

  • A criterion for determining whether multiple shells support a t-design

    Madoka Awada, Reina Ishikawa, Tsuyoshi Miezaki, Yuuho Tanaka

       2024.12

    Authorship：Lead author, Corresponding author

  • Equivariant theory for codes and lattices I

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki

       2024.12  [Refereed]

    Authorship：Lead author

  • Galois points for a finite graph

    Satoru Fukasawa, Tsuyoshi Miezaki

       2024.12  [Refereed]

    Authorship：Lead author

  • A note on the Assmus--Mattson theorem for some ternary codes

    Eiichi Bannai, Tsuyoshi Miezaki, Hiroyuki Nakasora

    Applicable Algebra in Engineering, Communication and Computing    2024.12  [Refereed]

    Authorship：Lead author

  • On the cycle index and the weight enumerator II

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura

    Journal of Algebra and Its Applications    2024.12  [Refereed]

    Authorship：Lead author

  • On the support t-designs of extremal Type III and IV codes

    Tsuyoshi Miezaki, Hiroyuki Nakasora

    Applicable Algebra in Engineering, Communication and Computing    2024.12  [Refereed]

    Authorship：Lead author

  • Harmonic Tutte polynomials of matroids II

    Thomas Britz, Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Reina Ishikawa

    Designs, Codes and Cryptography   92 ( 5 ) 1279 - 1297  2024.05  [Refereed]

    Authorship：Lead author

  • Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes

    Tsuyoshi Miezaki, Akihiro Munemasa

    Designs, Codes and Cryptography   92 ( 4 ) 1041 - 1049  2024.04  [Refereed]

    Authorship：Lead author

  • A note on a t-design in isodual codes

    Madoka Awada, Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

    Finite Fields and Their Applications   95  2024.03  [Refereed]

    Authorship：Lead author

  • Weighted Tutte--Grothendieck polynomials for graphs

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Chong Zheng

    Graphs and Combinatorics   39 ( 5 )  2023.10  [Refereed]

    Authorship：Lead author

  • A note on the Assmus--Mattson theorem for some binary codes II

    Eiichi Bannai, Tsuyoshi Miezaki, Hiroyuki Nakasora

    Designs, Codes and Cryptography   91   2509 - 2522  2023.07  [Refereed]

    Authorship：Lead author

  • On the Assmus–Mattson type theorem for Type I and even formally self-dual codes

    Tsuyoshi Miezaki, Hiroyuki Nakasora

    Journal of Combinatorial Designs   31 ( 7 ) 335 - 344  2023.07  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    5
    Citation
    (Scopus)

  • Pseudo-normalized Hecke eigenform and its application to extremal 2-modular lattices

    Tsuyoshi Miezaki, Gabriele Nebe

    Journal of Number Theory   248   294 - 309  2023.07  [Refereed]

    Authorship：Lead author

  • Harmonic Tutte polynomials of matroids

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura

    Designs, Codes and Cryptography   91   2223 - 2236  2023.06  [Refereed]

    Authorship：Lead author

  • Jacobi polynomials and design theory I

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura, Yuuho Tanaka

    Discrete Mathematics   346 ( 6 ) 113339 - 113339  2023.06  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Weight enumerators, intersection enumerators and Jacobi polynomials II

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura

    Discrete Mathematics   345 ( 12 )  2022.12  [Refereed]

    Authorship：Lead author

  • Variants of Jacobi polynomials in coding theory

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki

      90   2583 - 2597  2022.11  [Refereed]

    Authorship：Lead author

  • A note on the Assmus--Mattson theorem for some binary codes

    Tsuyoshi Miezaki, Hiroyuki Nakasora

    Designs, Codes and Cryptography   90 ( 6 ) 1485 - 1502  2022.06  [Refereed]

    Authorship：Lead author

    　View Summary

    Let C be a four-weight binary code, which has all one vector. Furthermore, we assume that C supports t-designs for all weights obtained from the Assmus–Mattson theorem. We previously showed that t≤ 5. In the present paper, we show an analogue of this result in the cases of five and six-weight codes.

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Average of complete joint weight enumerators and self-dual codes

    Himadri Shekhar Chakraborty, Tsuyoshi Miezaki

    Designs, Codes, and Cryptography   89 ( 6 ) 1241 - 1254  2021  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over F and Z in terms of the compositions of n and their distributions in the codes. We also obtain a generalization of the representation for the average of g-fold complete joint weight enumerators of codes over F and Z . Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found. q k q k

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • A note on Assmus-Mattson type theorems

    Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

    Designs, Codes and Cryptography   89 ( 5 ) 843 - 858  2021  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    16
    Citation
    (Scopus)

  • Design-theoretic analogies between codes, lattices, and vertex operator algebras

    Tsuyoshi Miezaki

    Designs, Codes and Cryptography   89 ( 5 ) 763 - 780  2021  [Refereed]

    Authorship：Lead author

  • Tutte polynomial, complete invariant, and theta series

    Misaki Kume, Tsuyoshi Miezaki, Tadashi Sakuma, Hidehiro Shinohara

    Graphs and Combinatorics   37 ( 5 ) 1545 - 1558  2021  [Refereed]

    Authorship：Lead author

  • A construction of spherical 3-designs

    Tsuyoshi Miezaki

    Ukrainian Mathematical Journal    2021  [Refereed]

    Authorship：Lead author

  • On Eisenstein polynomials and zeta polynomials II

    Miezaki T

    International Journal of Number Theory   16 ( 1 ) 207 - 218  2020.02  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

  • A generalization of the Tutte polynomials

    Miezaki T

    Proceedings of the Japan Academy Series A: Mathematical Sciences   95 ( 10 ) 111 - 113  2019.12  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we introduce the concept of the Tutte polynomials of genus g and discuss some of its properties. We note that the Tutte polynomials of genus one are well-known Tutte polynomials. The Tutte polynomials are matroid invariants, and we claim that the Tutte polynomials of genus g are also matroid invariants. The main result of this paper and the forthcoming paper declares that the Tutte polynomials of genus g are complete matroid invariants.

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • The support designs of the triply even codes of length 48

    Tsuyoshi Miezaki, Hiroyuki Nakasora

    Journal of Combinatorial Designs   27 ( 11 ) 673 - 681  2019.11  [Refereed]

    Authorship：Lead author

  • On Eisenstein polynomials and zeta polynomials

    Miezaki T

    Journal of Pure and Applied Algebra   223 ( 10 ) 4153 - 4160  2019.10  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • On the cycle index and the weight enumerator

    Tsuyoshi Miezaki, Manabu Oura

    Designs, Codes and Cryptography   87 ( 6 ) 1237 - 1242  2019.04  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • New Invariants for Integral Lattices

    HAYASAKA Ryota, MIEZAKI Tsuyoshi, TOKI Masahiko

    Interdisciplinary Information Sciences   25 ( 1 ) 53 - 57  2019  [Refereed]

    Authorship：Lead author

    　View Summary

    <p>Let Λ be any integral lattice in Euclidean space. It has been shown that for every integer n>0, there is a hypersphere that passes through exactly n points of Λ. Using this result, we introduce new lattice invariants and give some computational results related to two-dimensional Euclidean lattices of class number one.</p>

    DOI CiNii

  • An upper bound of the value of of the support -designs of extremal binary doubly even self-dual codes

    Tsuyoshi Miezaki, Hiroyuki Nakasora

    DESIGNS CODES AND CRYPTOGRAPHY   79 ( 1 ) 37 - 46  2016.04  [Refereed]

    Authorship：Lead author

    　View Summary

    Let be an extremal binary doubly even self-dual code of length and be the support design of for a weight . We introduce the two numbers and : is the largest integer such that, for all wight, is a -design; denotes the largest integer such that there exists a such that is a -design. In this paper, we consider the possible values of and .

    DOI

    Scopus

    12
    Citation
    (Scopus)

  • Congruences for the Fourier coefficients of the Mathieu mock theta function

    Tsuyoshi Miezaki, Matthias Waldherr

    JOURNAL OF NUMBER THEORY   148   451 - 462  2015.03  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we study the congruences for the Fourier coefficients of the Mathieu mock theta function, which appears in the Mathieu moonshine phenomenon discovered by Eguchi, Ooguri, and Tachikawa. (C) 2014 Elsevier Inc. All rights reserved.

    DOI

    Scopus

  • Erratum to On the support designs of extremal binary doubly even self-dual codes (Des. Codes Cryptogr., (2016), 10.1007/s10623-012-9782-3)

    Naoyuki Horiguchi, Tsuyoshi Miezaki, Hiroyuki Nakasora

    Designs, Codes, and Cryptography   73 ( 3 ) 1027 - 1028  2014.12  [Refereed]

    Authorship：Lead author

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • On the support designs of extremal binary doubly even self-dual codes

    Naoyuki Horiguchi, Tsuyoshi Miezaki, Hiroyuki Nakasora

    DESIGNS CODES AND CRYPTOGRAPHY   72 ( 3 ) 529 - 537  2014.09  [Refereed]

    Authorship：Lead author

    　View Summary

    Let D be the support design of the minimum weight of an extremal binary doubly even self-dual [24m, 12m, 4m + 4] code. In this note, we consider the case when D becomes a t-design with t &gt;= 6.

    DOI J-GLOBAL

    Scopus

    10
    Citation
    (Scopus)

  • The McKay-Thompson series of Mathieu Moonshine modulo two

    Thomas Creutzig, Gerald Hoehn, Tsuyoshi Miezaki

    RAMANUJAN JOURNAL   34 ( 3 ) 319 - 328  2014.08  [Refereed]

    Authorship：Lead author

    　View Summary

    In this note, we describe the parity of the coefficients of the McKay-Thompson series of Mathieu moonshine. As an application, we prove a conjecture of Cheng, Duncan, and Harvey stated in connection with umbral moonshine for the case of Mathieu moonshine.

    DOI J-GLOBAL

    Scopus

    3
    Citation
    (Scopus)

  • ON THE EXISTENCE OF EXTREMAL TYPE II Z(2k)-CODES

    Masaaki Harada, Tsuyoshi Miezaki

    MATHEMATICS OF COMPUTATION   83 ( 287 ) 1427 - 1446  2014.05  [Refereed]

    Authorship：Lead author

    　View Summary

    For lengths 8, 16, and 24, it is known that there is an extremal Type II Z(2k)-code for every positive integer k. In this paper, we show that there is an extremal Type II Z(2k)-code of lengths 32, 40, 48, 56, and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II Z(4k)-code for every positive integer k with k &gt;= 2.

    DOI J-GLOBAL

    Scopus

    4
    Citation
    (Scopus)

  • On a generalization of spherical designs

    Tsuyoshi Miezaki

    DISCRETE MATHEMATICS   313 ( 4 ) 375 - 380  2013.02  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we define the concept of a spherical T-design for a finite subset of a sphere. Then, we give some examples of such designs using the Z(2)-lattice, which is related to Lehmer's conjecture. (C) 2012 Elsevier B.V. All rights reserved.

    DOI J-GLOBAL

    Scopus

    4
    Citation
    (Scopus)

  • Conformal designs and DH Lehmer's conjecture

    Tsuyoshi Miezaki

    JOURNAL OF ALGEBRA   374   59 - 65  2013.01  [Refereed]

    Authorship：Lead author

    　View Summary

    In 1947, Lehmer conjectured that the Ramanujan tau-function tau(m) is non-vanishing for all positive integers m, where tau(m) are the Fourier coefficients of the cusp form Delta of weight 12. It is known that Lehmer's conjecture can be reformulated in terms of spherical t-design, by the result of Venkov. In this paper, we show that tau(m) = 0 is equivalent to the fact that the homogeneous space of the moonshine vertex operator algebra (V-b)(m+1) is a conformal 12-design. Therefore, Lehmer's conjecture is now reformulated in terms of conformal t-designs. (c) 2012 Elsevier Inc. All rights reserved.

    DOI J-GLOBAL

    Scopus

    10
    Citation
    (Scopus)

  • Frames in the odd Leech lattice

    Tsuyoshi Miezaki

    JOURNAL OF NUMBER THEORY   132 ( 12 ) 2773 - 2778  2012.12  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we show that there is a frame of norm k in the odd Leech lattice for every k &gt;= 3. (C) 2012 Elsevier Inc. All rights reserved.

    DOI J-GLOBAL

    Scopus

    2
    Citation
    (Scopus)

  • On a property of 2-dimensional integral Euclidean lattices

    Eiichi Bannai, Tsuyoshi Miezaki

    JOURNAL OF NUMBER THEORY   132 ( 3 ) 371 - 378  2012.03  [Refereed]

    Authorship：Lead author

    　View Summary

    Let Lambda be any integral lattice in the 2-dimensional Euclidean space. Generalizing the earlier works of Hiroshi Maehara and others, we prove that for every integer n &gt; 0, there is a circle in the plane R-2 that passes through exactly n points of Lambda. (C) 2011 Elsevier Inc. All rights reserved.

    DOI J-GLOBAL

    Scopus

    4
    Citation
    (Scopus)

  • On the Mathieu mock theta function

    Tsuyoshi Miezaki

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   88 ( 2 ) 28 - 30  2012.02  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper, we study the congruences of the Fourier coefficients of the Mathieu mock theta function, which appears in the Mathieu moonshine phenomenon discovered by Eguchi, Ooguri, and Tachikawa.

    DOI J-GLOBAL

    Scopus

    3
    Citation
    (Scopus)

  • On Euclidean designs and potential energy

    Tsuyoshi Miezaki, Makoto Tagami

    ELECTRONIC JOURNAL OF COMBINATORICS   19 ( 1 )  2012.01  [Refereed]

    Authorship：Lead author

    　View Summary

    We study Euclidean designs from the viewpoint of the potential energy. For a finite set in Euclidean space, we formulate a linear programming bound for the potential energy by applying harmonic analysis on a sphere. We also introduce the concept of strong Euclidean designs from the viewpoint of the linear programming bound, and we give a Fisher type inequality for strong Euclidean designs. A finite set on Euclidean space is called a Euclidean a-code if any distinct two points in the set are separated at least by a. As a corollary of the linear programming bound, we give a method to determine an upper bound on the cardinalities of Euclidean a-codes on concentric spheres of given radii. Similarly we also give a method to determine a lower bound on the cardinalities of Euclidean t-designs as an analogue of the linear programming bound.

  • An optimal odd unimodular lattice in dimension 72

    Masaaki Harada, Tsuyoshi Miezaki

    ARCHIV DER MATHEMATIK   97 ( 6 ) 529 - 533  2011.12  [Refereed]

    Authorship：Lead author

    　View Summary

    It is shown that if there is an extremal even unimodular lattice in dimension 72, then there is an optimal odd unimodular lattice in that dimension. Hence, the first example of an optimal odd unimodular lattice in dimension 72 is constructed from the extremal even unimodular lattice which has been recently found by G. Nebe.

    DOI J-GLOBAL

    Scopus

    5
    Citation
    (Scopus)

  • An elementary approach to toy models for Lehmer's conjecture

    Eiichi Bannai, Tsuyoshi Miezaki, Vladimir A. Yudin

    Izvestiya. Mathematics   75 ( 6 ) 1093 - 1106  2011.06  [Refereed]

    Authorship：Lead author

  • An elementary approach to toy models for D. H. Lehmer's conjecture

    E. Bannai, T. Miezaki, V. A. Yudin

    Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya   75 ( 6 ) 3 - 16  2011  [Refereed]

    Authorship：Lead author

    　View Summary

    We use the theory of algebraic fields to establish that none of the shells of the lattice Z(2) (resp. A(2)) is a 4-design (resp. 6-design). We discuss the connection between spherical designs and imaginary quadratic fields.

    DOI

    Scopus

    4
    Citation
    (Scopus)

  • An upper bound on the minimum weight of Type II Z(2k)-codes

    Masaaki Harada, Tsuyoshi Miezaki

    JOURNAL OF COMBINATORIAL THEORY SERIES A   118 ( 1 ) 190 - 196  2011.01  [Refereed]

    Authorship：Lead author

    　View Summary

    In this paper we give a new upper bound on the minimum Euclidean weight of Type II Z(2k)-codes and the concept of extremality for the Euclidean weights when k = 3 4 5 6 Together with the known result we demonstrate that there is an extremal Type II Z(2k)-code of length 8m (m &lt;= 8) when k = 3,4,5 6 (C) 2010 Elsevier Inc All rights reserved

    DOI J-GLOBAL

    Scopus

    5
    Citation
    (Scopus)

  • Toy models for D. H. Lehmer's conjecture

    Eiichi Bannai, Tsuyoshi Miezaki

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   62 ( 3 ) 687 - 705  2010.07  [Refereed]

    Authorship：Lead author

    　View Summary

    In 1947, Lehmer conjectured that the Ramanujan tau-function tau(m) never vanishes for all positive integers m, where tau(m) are the Fourier coefficients of the cusp form Delta(24) of weight 12. Lehmer verified the conjecture in 1947 for m &lt; 214928639999. In 1973, Serre verified up to m &lt; 10(15), and in 1999, Jordan and Kelly for m &lt; 22689242781695999.
    The theory of spherical t-design, and in particular those which are the shells of Euclidean lattices, is closely related to the theory of modular forms, as first shown by Venkov in 1984. In particular, Ramanujan's tau-function gives the coefficients of a weighted theta series of the E-8-lattice. It is shown, by Venkov, de la Harpe, and Pache, that tau(m) = 0 is equivalent to the fact that the shell of norm 2m of the E-8-lattice is an 8-design. So, Lehmer's conjecture is reformulated in terms of spherical t-design.
    Lehmer's conjecture is difficult to prove, and still remains open. In this paper, we consider toy models of Lehmer's conjecture. Namely, we show that the m-th Fourier coefficient of the weighted theta series of the Z(2)-lattice and the A(2)-lattice does not vanish, when the shell of norm in of those lattices is not the empty set. In other words, the spherical 5 (resp. 7)-design does not exist among the shells in the Z(2)-lattice (resp. A(2)-lattice).

    DOI J-GLOBAL

    Scopus

    14
    Citation
    (Scopus)

  • Toy models for D.H. Lehmer's conjecture

    Eiichi Bannai, Tsuyoshi Miezaki

    Journal of the Mathematical Society of Japan   62 ( 3 ) 687 - 705  2010.03  [Refereed]

    Authorship：Lead author

  • Nonexistence for extremal Type II Z_2k-Codes

    Tsuyoshi Miezaki

    Kumamoto Journal of Mathematics   23   27 - 35  2010  [Refereed]

    Authorship：Lead author

    CiNii

  • Codes, Lattices, Vertex Operator Algebras, from the viewpoint of Design Theory and Modular Forms

       2009.03  [Refereed]

    Authorship：Lead author

  • On the zeros of Hecke-type faber polynomials

    Eiichi Bannai, Koji Kojima, Tsuyoshi Miezaki

    KYUSHU JOURNAL OF MATHEMATICS   62 ( 1 ) 15 - 61  2008.03  [Refereed]

    Authorship：Lead author

    　View Summary

    For any McKay-Thompson series which appear in Moonshine, the Hecke-type Faber polynomial dagger P-n (X) of degree n is defined. The Hecke-type Faber polynomials are of course special cases of the Faber polynomials introduced by Faber a century ago. We first study the locations of the zeros of the Hecke-type Faber polynomials of the 171 monstrous types, as well as those of the 157 non-monstrous types. We have calculated, using a computer, the zeros for all n &lt;= 50. These results suggest that in many (about 13%) of the cases, we can expect that all of the zeros of P-n (x) are real numbers. In particular, we prove rigorously that the zeros of the Hecke-type Faber polynomials (of any degree) for the McKay-Thompson series of type 2A are real numbers. We also discuss the effect of the existence of harmonics, and the effect of a so-called dash operator. We remark that by the dash operators, we obtain many replicable functions (with rational integer coefficients) which are not necessarily completely replicable functions. Finally, we study more closely the curves on which the zeros of the Hecke-type Faber polynomials for type 5B lie in particular in connection with the fundamental domain (on the upper half plane) of the group Gamma(0)(5), which was studied by Shigezumi and Tsutsumi. At the end, we conclude this paper by stating several observations and speculations.

    DOI J-GLOBAL

    Scopus

    1
    Citation
    (Scopus)

  • On the zeros of Eisenstein series for Gamma(*)(0)(2) and Gamma(*)(0)(3)

    Tsuyoshi Miezaki, Hiroshi Nozaki, Junichi Shigezumi

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   59 ( 3 ) 693 - 706  2007.07  [Refereed]

    Authorship：Lead author

    　View Summary

    We locate all of the zeros of the Eisenstein series associated with the Fricke groups Gamma(0)*(2) and Gamma(0)*(3) in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer ("On the zeros of Eisenstein series", 1970).

    DOI J-GLOBAL

    Scopus

    29
    Citation
    (Scopus)

  • Question and Answer Check System for Mathematics on the Web

    Seiichi Toyota, Tsuyoshi Miezaki, Masakazu Suzuki

    Proceedings of the Seventh Asian Symposium on Computer Mathematics     263 - 266  2005  [Refereed]

    Authorship：Lead author

▼display all

Presentations

  • A generalization of the Tutte polynomials

     [Invited]

    P-positivity in Matroid Theory and related Topics 

    Presentation date： 2021.10

  • 符号，格子と頂点作用素代数におけるレーマー型問題

     [Invited]

    第66回 代数学シンポジウム 

    Presentation date： 2021.09

  • タット多項式とコンウェイの問題の高次数化

     [Invited]

    早稲田整数論セミナー 

    Presentation date： 2021.04

  • Recent advances in matroids and Tutte polynomials

    Tsuyoshi Miezaki  [Invited]

    A generalization of the Tutte polynomials 

    Presentation date： 2019.07

  • 神楽坂代数セミナー

    Tsuyoshi Miezaki  [Invited]

    マシュー群に関係するモックテータ関数のフーリエ係数について 

    Presentation date： 2018.12

  • 数理経済談話会

    Tsuyoshi Miezaki  [Invited]

    タット多項式の高種数化 

    Presentation date： 2018.11

  • タット多項式の高種数化

    Tsuyoshi Miezaki, Manabu Oura, Tadashi Sakuma, Hidehiro Shinohara

    日本数学会秋季総合分科会 

    Presentation date： 2018.09

  • 完全巡回指数の導入

    Tsuyoshi Miezaki, Manabu Oura  [Invited]

    日本数学会秋季総合分科会 

    Presentation date： 2018.09

  • 大阪組合せ論セミナー

    Tsuyoshi Miezaki  [Invited]

    デザイン理論について 

    Presentation date： 2016.06

  • Intersection of Pure Mathematics and Applied Mathematics VIII: Special

    Tsuyoshi Miezaki  [Invited]

    2次形式の表現数と符号理論 

    Presentation date： 2015

  • Intersection of Pure Mathematics and Applied Mathematics VIII: Special

    Tsuyoshi Miezaki

    2次形式の表現数と符号理論 

    Presentation date： 2015

▼display all

Research Projects

  • 離散構造における不変量と対称性

    日本学術振興会  科学研究費補助金

    Project Year :

    2022.04
    -
    2026.03
     

  • 保型形式および多項式不変量を用いた対称性の探求

    日本学術振興会  科学研究費助成事業

    Project Year :

    2018.04
    -
    　
     

    三枝崎 剛

    　View Summary

    符号と格子、そして頂点作用素代数の類似性はよく知られている。本課題では、これらの類似性に着目し、主にデザイン理論と不変量の二つの視点から研究を行った。
    符号から得られる t-デザインの t 値は 5 以下と予想されている。同様に格子や頂点作用素代数から得られる t-デザインの t 値は 11 以下と予想されている。符号の場合に t 値が 6 以上、格子や頂点作用素代数の場合に t 値が 12 以上の例を発見することをは、有限群論や整数論からも重要な問題と認識されている。
    宗政昭弘（東北大）、中空大幸（神戸学院大学）との共同研究で、ある符号から 1-デザインが得られ、さらに特別な重さの符号語から 2-デザインが得られることを示した。格子類似も同様に得られ、海外誌に発表されている。こちらの頂点作用素代数類似やその他の類似性の研究も海外誌に発表した。
    Himadri Chakraborty（Shahjalal University of Science and Technology）との共同研究で、符号の交叉平均重み多項式、交叉数という不変量を導入し、性質を調べた。こちらも海外誌に発表されている。
    中空大幸（神戸学院大学）との共同研究で、特別な k に対し、k-weight 符号（さらにある条件が付く）という条件下で符号から得られる t-デザインの t 値は 5 以下を確認した。こちらも海外誌に発表済である。この問題の背景には楕円曲線、あるいはさらに高次の曲線の整数解と関係があることが最近になって判明し、現在こちらも論文を執筆中である。

  • A study of symmetry using the theory of automorphic forms

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2015.04
    -
    2018.03
     

    MIEZAKI Tsuyoshi

    　View Summary

    The purpose of this study is the classification of the codes, the lattices, and the vertex operator algebras, from the point of view of the automorphic forms and the design theory.

  • E-polynomials and combinatorics

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2017.04
    -
    　
     

    Oura Manabu

    　View Summary

    We studied algebraic combinatorics widely. We consider the ring generated by the g-th weight enumerators of self-dual and doubly even codes of dn+. It is finitely generated over the complex numbers C and we determined the generators for g=1,2. We gave the relation between the g-th weight enumerators and the complete cycle index of the permutation group obtained from codes. We studied Duursma's zeta polynomial of E-polynomials. We defined the g-th Tutte polynomials and studied its properties. We generalized Ozeki's Jacobi polynomials. We discussed the concept of E-polynomials in classical invariant theory.

  • 有限群と格子を用いた球デザインの構成

    日本学術振興会  科学研究費助成事業

    Project Year :

    2014.04
    -
    2017.03
     

  • 保型形式を用いた対称性の探求

    山形大学  住友財団 基礎科学研究助成

    Project Year :

    2014.10
    -
    2016.09
     

  • 符号，格子及び頂点作用素代数の対称性

    科学研究費助成事業

    Project Year :

    2012.04
    -
    2016.03
     

    三枝崎剛

  • Symmetry of Codes, Lattices, and Vertex operator algebras

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2012.04
    -
    2015.03
     

    MIEZAKI Tsuyoshi

    　View Summary

    The purpose of this study is the classification of the codes, the lattices, and the vertex operator algebras from the point of view of the modular forms and the design theory.

  • Research on codes, lattices, and vertex operator algebras using design theory

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2010.04
    -
    2012.03
     

    MIEZAKI Tsuyoshi

    　View Summary

    Codes, Lattices, and Vertex Operator Algebras are important mathematical objects with many similar properties. For example, designs and minimum distances are defined on the three objects. Originally, the coding theory was introduced for the purpose of communication, hence, it has wide application in real life. In this study, I investigated some property of the three objects for some cases. For example, I determined the minimum bounds and classified t-designs for some cases.

  • デザイン理論を用いた符号・格子及び頂点作用素代数の研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2011
    　
    　
     

    三枝崎 剛

  • Research on codes, lattices, and vertex operator algebras using design theory

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2010
    -
    2011
     

    MIEZAKI Tsuyoshi

    　View Summary

    Codes, Lattices, and Vertex Operator Algebras are important mathematical objects with many similar properties. For example, designs and minimum distances are defined on the three objects. Originally, the coding theory was introduced for the purpose of communication, hence, it has wide application in real life. In this study, I investigated some property of the three objects for some cases. For example, I determined the minimum bounds and classified t-designs for some cases.

  • 保型形式及びFaber多項式の零点配置と球面上の代数的組合せ論に関する研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2008.04
    -
    2010.03
     

    三枝崎剛

    　View Summary

    符号,格子及び頂点作用素代数について,組合せ論の立場から考察し,研究を行った.
    格子から構成される球面デザインの非存在を証明した.球面t-デザインとは,球面上の有限集合で,ある条件を満たすものである.一般に,t-デザインならば(t-1)-デザインになり,高いtのt-デザインを見つけることが,目標である.例えばE8格子の原点から等距離にある点集合は,球面上に存在しており,その集合は,7-デザインになっている事が知られている.では,8-デザイン以上になるか否かは,非常に興味ある問題である.ここで,非常に面白い事に,この問題は数論で古くから未解決である,レーマー予想と同値になっているのである.今年度,特別なの2次元整数格子に対して,デザインの非存在を証明出来た.具体的には,2次元整数格子は虚二次体の整環とみなす事が出来るが,類数1,2の整環に対応する格子に対して,デザインの非存在を証明した.
    4次直交群の有限部分群から構成される球面t-デザインのtの値を決定した.直交群の有限部分群の軌道は,自然に球面上に存在していると考えられるが,そうして構成されるt-デザインの,tの値は余り高くならない事が予想されている.この予想を確認するべく,今回は,最近になって分類が完成した4次直交群の有限部分群全てに対して,t-デザインとなるtの値を決定した.
    共形デザインの非存在を証明した.近年,頂点作用素代数(以下VOAと略す)上に共形t-デザインという概念が定義された.例えば頂点作用素代数の最も重要な例である,ムーンシャインVOAは,共形11-デザインを構成する事が知られている.更に,球面デザインの時と同じく,12-デザインになるか否かは,レーマー予想と同値になる.研究代表者は,自由ボゾン型VOAに関して,デザインの非存在を示した.更に,格子VOAに関しても,非存在を示すべく研究中である.

  • 保型形式及びFaber多項式の零点配置と球面上の代数的組合せ論に関する研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2008
    -
    2010
     

    三枝崎剛

▼display all

Misc

▼display all

 

Syllabus

▼display all

Teaching Experience

  • 幾何学特論A演習

    琉球大学  

  • 幾何学特論A

    琉球大学  

  • 卒業研究

    琉球大学  

  • 微分積分学入門I

    琉球大学  

  • 数の文化

    琉球大学  

  • 微分積分学入門II

    琉球大学  

  • 幾何学特論B演習

    琉球大学  

  • 幾何学特論B

    琉球大学  

  • 幾何学序論II演習

    琉球大学  

  • 幾何学序論II

    琉球大学  

▼display all

 

Social Activities

  • 教員免許更新講習（身の回りにある対称性の観察）

    2019.07
    -
    　

  • 教員免許更新講習（結び目理論の紹介）

    2019.07
    -
    　

  • ひらめき☆ときめきサイエンスー結び目の数学ー

    日本学術振興会  琉球新報 

    2018.08
    -
    　

  • 公開講座

    琉球大学 

    2018.07
    -
    　

  • 数学オリンピック財団主催夏季セミナー講師

    数学オリンピック財団  （ヴィラ千ヶ滝,.） 

    2012.08
    -
    　

Sub-affiliation

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2022
    -
    2024

    Waseda Research Institute for Science and Engineering   Concurrent Researcher

Internal Special Research Projects

  • 離散構造における不変量と対称性 研究課題

    2023  

    　View Summary

    研究について：１．符号から得られるt-デザイン構造の解析：対称性の高い符号からt-デザイン構造を得ることができる。本研究は、III型・IV型，平方剰余符号，拡大平方剰余符号というクラスから、高いtのt-デザイン構造を得ることに成功した。２．グラフの完全不変量の構築：スタンレーの彩色対称関数はグラフの不変量だが、完全不変量でない。本研究では不変グラフ族という概念を導入し、彩色対称関数をより強力にし、グラフの完全不変量を構築した。教育について：近年、スペクトラル・グラフ理論は多くの応用数学分野に現れ注目される対象となっている。しかし日本語で書かれた書籍は存在しない。そこで洋書を翻訳し、出版に至った。これを用いて、ゼミや授業を行う計画である。