On the evaluation at (i,i) of the Tutte polynomial of a binary matroid
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 $\zfour$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.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 arXiv:
 arXiv:1203.0910
 Bibcode:
 2012arXiv1203.0910P
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 10 pages