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Journal Articles Journal of Algebraic Combinatorics Year : 2007

On the evaluation at $(j,j^2)$ of the Tutte polynomial of a ternary matroid

Abstract

F. Jaeger has shown that up to a $\pm$ sign the evaluation at $(j,j^2)$ of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over $GF(3)$. We give a short algebraic proof of this result, which moreover yields the exact value of $\pm$, a problem left open in Jaeger's paper. It follows that the computation of $t(j,j^2)$ is of polynomial complexity for a ternary matroid.

Dates and versions

lirmm-00154516 , version 1 (13-06-2007)

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Emeric Gioan, Michel Las Vergnas. On the evaluation at $(j,j^2)$ of the Tutte polynomial of a ternary matroid. Journal of Algebraic Combinatorics, 2007, 25 (1), pp.1-6. ⟨10.1007/s10801-006-0035-2⟩. ⟨lirmm-00154516⟩
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