Geodesic
On the evaluation at $(j,j^2)$ of the Tutte polynomial of a ternary matroid
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 1, pp. 1-6.

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Summary: 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.
Keywords: keywords matroid, ternary matroid, tutte polynomial, graph, knot theory, Jones polynomial, computational complexity 
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Gioan, Emeric; Las Vergnas, Michel. On the evaluation at $(j,j^2)$ of the Tutte polynomial of a ternary matroid. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 1, pp. 1-6. http://geodesic.mathdoc.fr/item/JAC_2007__25_1_a5/