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
SN - 0925-9899
VL - 39
SP - 141
EP - 152
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -