Discrete Mathematics & Theoretical Computer Science (Jan 2014)

The arithmetic Tutte polynomials of the classical root systems

  • Federico Ardila,
  • Federico Castillo,
  • Michael Henley

DOI
https://doi.org/10.46298/dmtcs.2447
Journal volume & issue
Vol. DMTCS Proceedings vol. AT,..., no. Proceedings

Abstract

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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.

Keywords