Tutte Polynomial, Complete Invariant, and Theta Series

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


研究成果: Article査読


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.

ジャーナルGraphs and Combinatorics
出版ステータスAccepted/In press - 2020

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


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