An Approach to Symmetry Using Modular Forms and Polynomial Invariants

• Project/Area Number: 18K03217
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Waseda University (2021-2022); University of the Ryukyus (2018-2020)
• Principal Investigator: Miezaki Tsuyoshi 早稲田大学, 理工学術院, 教授 (60584068)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Discontinued (Fiscal Year 2022)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 符号 / 格子 / 頂点作用素代数 / マトロイド / グラフ / 重さ多項式 / テータ級数 / 組合せデザイン / 不変量 / タット多項式 / 完全不変量 / アスマスマトソンの定理 / デザイン理論 / モジュラー形式 / サイクル多項式 / ゼータ多項式 / 保型形式 / 多項式不変量

Outline of Final Research Achievements

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.

Academic Significance and Societal Importance of the Research Achievements

本研究の成果は，主に符号や格子，頂点作用素代数，さらにはマトロイドやグラフの分類問題に関するものである．符号はもともと情報伝達の効率化・高精度化を目標に導入された概念である．したがって本研究の成果は数学的にも，実生活への応用上も重要なものである．

Research Products

• [Int'l Joint Research] SUST(バングラデシュ)
• [Journal Article] Design-theoretic analogies between codes, lattices, and vertex operator algebras (2021)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Designs, Codes and Cryptography Volume: 89 Issue: 5 Pages: 763-780
  • DOI: 10.1007/s10623-021-00842-2
  • Peer Reviewed
• [Journal Article] A note on Assmus-Mattson type theorems (2021)
  • Author(s): Tsuyoshi Miezaki, Akihiro Munemasa & Hiroyuki Nakasora
  • Journal Title: Designs, Codes and Cryptography Volume: 89 Issue: 5 Pages: 843-858
  • DOI: 10.1007/s10623-021-00848-w
  • Peer Reviewed
• [Journal Article] Average of complete joint weight enumerators and self-dual codes (2021)
  • Author(s): Himadri Shekhar Chakraborty & Tsuyoshi Miezaki
  • Journal Title: Designs, Codes and Cryptography Volume: 89 Issue: 6 Pages: 1241-1254
  • DOI: 10.1007/s10623-021-00874-8
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Tutte Polynomial, Complete Invariant, and Theta Series (2020)
  • Author(s): Kume Misaki、Miezaki Tsuyoshi、Sakuma Tadashi、Shinohara Hidehiro
  • Journal Title: Graphs and Combinatorics Volume: online Issue: 5 Pages: 1-14
  • DOI: 10.1007/s00373-020-02238-w
  • Peer Reviewed
• [Journal Article] On Eisenstein polynomials and zeta polynomials II (2020)
  • Author(s): Tsuyoshi Miezaki, Manabu Oura
  • Journal Title: International Journal of Number Theory Volume: 1 Issue: 01 Pages: 207-218
  • DOI: 10.1142/s1793042120500116
  • Peer Reviewed / Open Access
• [Journal Article] The support designs of the triply even codes of length 48 (2019)
  • Author(s): Tsuyoshi Miezaki, Hiroyuki Nakasora
  • Journal Title: Journal of Combinatorial Designs Volume: 27 Issue: 11 Pages: 673-681
  • DOI: 10.1002/jcd.21670
  • Peer Reviewed
• [Journal Article] A generalization of the Tutte polynomials (2019)
  • Author(s): Tsuyoshi Miezaki, Manabu Oura, Tadashi Sakuma, Hidehiro Shinohara
  • Journal Title: Proceedings of the Japan Academy, Ser. A Mathematical Sciences Volume: 95 Issue: 10 Pages: 111-113
  • DOI: 10.3792/pjaa.95.111
  • NAID: 40022103495
  • Peer Reviewed / Open Access
• [Journal Article] On the cycle index and the weight enumerator (2018)
  • Author(s): Tsuyoshi Miezaki, Manabu Oura
  • Journal Title: Designs, Codes and Cryptography Volume: 印刷中 Issue: 6 Pages: 1237-1242
  • DOI: 10.1007/s10623-018-0518-x
  • Peer Reviewed / Open Access
• [Journal Article] On Eisenstein polynomails and zeta polynomials (2018)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Journal of Pure and Applied Algebra Volume: 印刷中 Issue: 10 Pages: 4153-4160
  • DOI: 10.1016/j.jpaa.2019.01.002
  • Peer Reviewed
• [Journal Article] New invariants for integral lattices (2018)
  • Author(s): Ryota Hayasaka, Tsuyoshi Miezaki, Masahiko Toki
  • Journal Title: Interdisciplinary Information Sciences Volume: 印刷中
  • NAID: 130007720021
  • Peer Reviewed
• [Presentation] A generalization of the Tutte polynomials (2021)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: P-positivity in Matroid Theory and related Topics
  • Int'l Joint Research / Invited
• [Presentation] 符号，格子と頂点作用素代数におけるレーマー型問題 (2021)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第66回 代数学シンポジウム
  • Invited
• [Presentation] A generalization of the Tutte polynomials (2019)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Recent advances in matroids and Tutte polynomials
  • Int'l Joint Research / Invited
• [Presentation] 完全巡回指数の導入 (2018)
  • Author(s): 三枝崎剛
  • Organizer: 日本数学会・2018年度秋季総合分科会
  • Invited
• [Presentation] タット多項式の高種数化 (2018)
  • Author(s): 三枝崎剛
  • Organizer: 日本数学会・2018年度秋季総合分科会
  • Invited
• [Presentation] 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 (2018)
  • Author(s): 三枝崎剛
  • Organizer: 神楽坂代数セミナー
• [Presentation] タット多項式の高種数化 (2018)
  • Author(s): 三枝崎剛
  • Organizer: 数理経済談話会
• [Remarks] Tsuyoshi Miezaki
  • URL: https://sites.google.com/site/tmiezaki/
• [Remarks] Tsuyoshi Miezaki
  • URL: http://www.f.waseda.jp/miezaki/index.html
• [Remarks] Tsuyoshi Miezaki's website
  • URL: https://sites.google.com/site/tmiezaki/
• [Remarks] 三枝崎剛のホームページ
  • URL: https://sites.google.com/site/tmiezakij/