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 exactly determine $T_M(-\iota,\iota)$, and show how to evaluate this number in polynomial time. In particular, we describe how the argument of the complex number $T_M(-\iota,\iota)$ depends on a certain Z mod four valued quadratic form that is canonically associated with M.
Original languageEnglish
Publishers.n.
Number of pages9
Publication statusPublished - 2012

Publication series

NamearXiv.org
Volume1203.0910 [math.CO]

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