JOURNAL OF
ALGEBRAIC
COMBINATORICS

Home > Vol 25, No 1 (2007)

Emeric Gioan¹ and Michel Las Vergnas²

¹Université Montpellier 2, LIRMM 161 rue Ada 34392 Montpellier cedex 5 France
²Université Pierre et Marie Curie (Paris 6) case 189 - Combinatoire \& Optimisation 4 place Jussieu 75005 Paris France

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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5. D. Vertigan, “Bicycle dimension and special points of the Tutte Polynomial,” J. Comb. Theory B74 (1998), 378-396.