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.
|Number of pages||9|
|Publication status||Published - 2012|