Authors: Federico Ardila ^1,2; Federico Castillo ^3,4; Michael Henley ⁵

• 1 Department of Mathematics [San Francisco]
• 2 Universidad de los Andes [Bogota]
• 3 Universidad de los Andes [Bogota]
• 4 University of California [Davis]
• 5 San Francisco State University

Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric 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 \emphfinite field method for arithmetic Tutte polynomials, and by enumerating signed graphs with respect to six parameters.