On the evaluation at (j, j2) of the Tutte polynomial of a ternary matroid
نویسندگان
چکیده
F. Jaeger has shown that up to a ± sign the evaluation at ( j, j2) of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over G F(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, j2) is of polynomial complexity for a ternary matroid.
منابع مشابه
Tutte Polynomials and Bicycle Dimension of Ternary Matroids
Let M be a ternary matroid, t(M,x,y) be its Tutte polynomial and d(M) be the dimension of the bicycle space of any representation of M over GF(3) . We show that, for j = e2'"/3, the modulus of the complex number t(M,j,j2) is equal to (v/3)'/(M) . The proof relies on the study of the weight enumerator Wv\y) of the cycle space £* of a representation of M over GF(3) evaluated at y = j . The main t...
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