The arithmetic Tutte polynomials of the classical root systems

Federico Ardila (1, 2) , Federico Castillo (2, 3) , Michael Henley (4)

1 Department of Mathematics [San Francisco]
2 UNIANDES - Universidad de los Andes [Bogota]
3 UC Davis - University of California [Davis]
4 SFSU - 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.

Mots clés: Root systems; Toric arrangements; Tutte polynomials; Rogers-Ramanujan function; Signed graphs

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Federico Ardila, Federico Castillo, Michael Henley. The arithmetic Tutte polynomials of the classical root systems. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.851-862, ⟨10.46298/dmtcs.2447⟩. ⟨hal-01207564⟩