On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid

Details On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid

2012-03-05

arxiv.org/abs/1203.0910v1

Mathematics

Combinatorics

Scientific paper

Vertigan has shown that if M is a binary matroid, then |T_M(-i,i)|, the modulus of the Tutte polynomial of M as evaluated in (-i, i), can be expressed in terms of the bicycle dimension of M. In this paper, we exactly determine T_M(-i,i), and show how to evaluate this number in polynomial time. In particular, we describe how the argument of the complex number T_M(-i,i) depends on a certain Z mod four valued quadratic form that is canonically associated with M.

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