Tutte polynomial, complete invariant, and theta series
Combinatorics
2020-10-06 v4 Number Theory
Abstract
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 L_1 and L_2 be two non-isomorphic lattices. We state that L_1 and L_2 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.
Cite
@article{arxiv.2007.15089,
title = {Tutte polynomial, complete invariant, and theta series},
author = {Misaki Kume and Tsuyoshi Miezaki and Tadashi Sakuma and Hidehiro Shinohara},
journal= {arXiv preprint arXiv:2007.15089},
year = {2020}
}
Comments
13 pages, 1 figure