TY - JOUR

T1 - On the evaluation at $(-\iota,\iota)$ of the Tutte polynomial of a binary matroid

AU - Pendavingh, R.A.

PY - 2014

Y1 - 2014

N2 - 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 $\mathbb{Z}_4$-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.

AB - 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 $\mathbb{Z}_4$-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.

U2 - 10.1007/s10801-013-0442-0

DO - 10.1007/s10801-013-0442-0

M3 - Article

VL - 39

SP - 141

EP - 152

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 1

ER -