Invariants for discrete mathematics

Reference No.	2023a002
Type/Category	Grant for General Research-Workshop（Ⅱ）
Title of Research Project	Invariants for discrete mathematics
Principal Investigator	Tsuyoshi Miezaki（Faculty of Science and Engineering, Waseda University・Professor）
Research Period	June 22,2023. ～ June 22,2023.
Keyword(s) of Research Fields	Error-correcting code, lattice, hyperplane arrangement, graph, matroid, weight enumerator, Whitney polynomial, Tutte polynomial, characteristic quasi-polynomial
Abstract for Research Report	There are discrete structures closely related to each other: codes, lattices, hyperplane arrangements, graphs, and matroids. The five have many similar properties, such as the fact that lattices, hyperplane arrangements, graphs, and matroids can be constructed from codes, and there are many studies that take these similarities into account. The concept of codes was originally introduced as a method of information transmission and for the purpose of improving efficiency and has a wide range of applications in real life. Therefore, the problem of classification of the five is an important and mathematically interesting problem, both in terms of real-life applications and in terms of mathematics. One of the most effective classification methods is the use of polynomial invariants. For example, important invariants such as weight enumerators for codes, coboundary polynomials for hyperplane arrangements, and Tutte polynomials for graphs and matroids are defined, and very interestingly, they are known to relate each other by variable transformation. In recent years, the group of Tsuyoshi Miezaki, a member of the organizing committee, has made a significant progress in the study of polynomial invariants of codes, graphs, and matroids. For example, they gave a complete polynomial invariant of matroids, a complete invariant of graphs, weighted chromatic polynomials, the definition of Jacobi type polynomial invariants, and many other polynomial invariants that are expected to develop greatly in the future have been discovered. In this meeting, we aim to share these results with researchers in the groups of hyperplane arrangements, graphs, and matroids. For this purpose, we invite a wide range of researchers involved in both fields to present and discuss the latest research results in their respective fields, and we hope that new relationships between the two fields will be discovered.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Norihiro Nakashima（Nagoya Institute of Technology・Associate Professor） Manabu Oura（Kanazawa University・Professor）