Computing the Tutte polynomial of lattice path matroids using determinantal circuits

We give a quantum-inspired Opnq algorithm computing the Tutte polynomial of a lattice path matroid, where n is the size of the ground set of the matroid. Furthermore, this can be improved to Opnq arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was Opnq, and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems such as those that appear in simulating quantum systems. 2010 Mathematics Subject Classification. Primary: 05B35, 05A15.