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2012

On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid

Pendavingh, Rudi

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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 $\zfour$-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.

On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid · Around

Built on

Generalizations of the Kervaire invariant
Edgar H. Brown, Jr · 1972
Earlier work this paper cites.
Weight enumeration and the geometry of linear codes
Curtis Greene · 1976
Earlier work this paper cites.
On the principal edge tripartition of a graph
P. Rosenstiehl and R. C. Read · 1977
Earlier work this paper cites.
Practical graph isomorphism
Brendan D. McKay · 1981
Earlier work this paper cites.
Tutte polynomials and bicycle dimension of ternary matroids
François Jaeger · 1989
Earlier work this paper cites.

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