On the evaluation at \(( - \iota ,\iota )\) of the Tutte polynomial of a binary matroid (Q2441567)

The complexity of determining the value of the Tutte polynomial \(T(x,y)\) of a matroid for various choices of \((x,y)\) has been extensively examined. In this paper, it is shown that for binary matroids the evaluation \(T(-\iota,\iota)\) depends on a specific quadratic form associated with the matroid. Using this connection, the paper establishes that \(T(-\iota,\iota)\) can be computed in polynomial time for a binary matroid; related invariants are also computed. Finally the use of these invariants in isomorphism testing for matroids is discussed.