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

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