The Arithmetic Tutte Polynomials of the Classical Root Systems. (5th April 2014) - Ardila, Federico; Castillo, Federico; Henley, Michael
Abstract: Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a toric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems A n, B n, C n, and D n with respect to their integer, root, and weight lattices. We do it in two ways: by introducing a finite field method for arithmetic Tutte polynomials and by enumerating signed graphs with respect to six parameters.