On the evaluation at $(-\iota,\iota)$ of the Tutte polynomial of a binary matroid

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Abstract

Vertigan has shown that if $M$ is a binary matroid, then $|T_M(-\iota,\iota)|$, the modulus of the Tutte polynomial of $M$ as evaluated in $(-\iota, \iota)$, can be expressed in terms of the bicycle dimension of $M$. In this paper, we describe how the argument of the complex number $T_M(-\iota,\iota)$ depends on a certain $\mathbb{Z}_4$-valued quadratic form that is canonically associated with $M$. We show how to evaluate $T_M(-\iota,\iota)$ in polynomial time, as well as the canonical tripartition of $M$ and further related invariants.
Original languageEnglish
Pages (from-to)141-152
JournalJournal of Algebraic Combinatorics
Volume39
Issue number1
DOIs
Publication statusPublished - 2014

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