Tutte Polynomial, Complete Invariant, and Theta Series

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1545-1558
Number of pages14
JournalGraphs and Combinatorics
Issue number5
Publication statusPublished - 2021 Sept
Externally publishedYes


  • Code
  • Lattice
  • Matroid
  • Theta series
  • Tutte polynomial
  • Weight enumerator

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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