Geodesic
On the evaluation at $( - \iota ,\iota )$ of the Tutte polynomial of a binary matroid
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 141-152.

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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 $\mathbb{Z}/4\mathbb {Z}$-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.
Classification : 05B35, 05C31, 68Q17
Keywords: matroid, Tutte polynomial, computational complexity 
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     title = {On the evaluation at $( - \iota ,\iota )$ of the {Tutte} polynomial of a binary matroid},
     journal = {Journal of Algebraic Combinatorics},
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Pendavingh, R.A. On the evaluation at $( - \iota ,\iota )$ of the Tutte polynomial of a binary matroid. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 141-152. http://geodesic.mathdoc.fr/item/JAC_2014__39_1_a3/