On the evaluation at (−ι,ι) of the Tutte polynomial of a binary matroid

@article{Pendavingh2012OnTE,
title={On the evaluation at (−ι,ι) of the Tutte polynomial of a binary matroid},
author={R. Pendavingh},
journal={Journal of Algebraic Combinatorics},
year={2012},
volume={39},
pages={141-152}
}

Vertigan has shown that if M is a binary matroid, then |TM(−ι,ι)|, the modulus of the Tutte polynomial of M as evaluated in (−ι,ι), can be expressed in terms of the bicycle dimension of M. In this paper, we describe how the argument of the complex number TM(−ι,ι) depends on a certain $\mathbb{Z}/4\mathbb {Z}$-valued quadratic form that is canonically associated with M. We show how to evaluate TM(−ι,ι) in polynomial time, as well as the canonical tripartition of M and further related invariants.