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

摘要

F. Jaeger has shown that up to a ± 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 ±, 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.