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

Emeric Gioan 1 Michel Las Vergnas 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00154516
Contributor : Emeric Gioan <>
Submitted on : Wednesday, June 13, 2007 - 11:12:58 PM
Last modification on : Saturday, April 11, 2020 - 2:06:50 AM

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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, Springer Verlag, 2007, 25 (1), pp.1-6. ⟨10.1007/s10801-006-0035-2⟩. ⟨lirmm-00154516⟩

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