Tutte Polynomial, Complete Invariant, and Theta Series

Misaki Kume, Tsuyoshi Miezaki*, Tadashi Sakuma, Hidehiro Shinohara

*この研究の対応する著者

研究成果: Article査読

抄録

In this study, we present two results that relate Tutte polynomials. First, we provide new and complete polynomial invariants for graphs. We note that the number of variables of our polynomials is one. Second, let L1 and L2 be two non-isomorphic lattices. We state that L1 and L2 are theta series equivalent if those theta series are the same. The problem of identifying theta series equivalent lattices is discussed in Prof. Conway’s book The Sensual (Quadratic) Form with the title “Can You Hear the Shape of a Lattice?” In this study, we present a method to find theta series equivalent lattices using matroids and their Tutte polynomials.

本文言語English
ジャーナルGraphs and Combinatorics
DOI
出版ステータスAccepted/In press - 2020
外部発表はい

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学

フィンガープリント

「Tutte Polynomial, Complete Invariant, and Theta Series」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル