Federico Ardila ; Federico Castillo ; Michael Henley
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The arithmetic Tutte polynomials of the classical root systems
dmtcs:2447 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2014,
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
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https://doi.org/10.46298/dmtcs.2447
The arithmetic Tutte polynomials of the classical root systemsConference paper
Authors: Federico Ardila 1,2; Federico Castillo 3,4; Michael Henley 5
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 <i>arithmetic</i> Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems An,Bn,Cn, and Dn 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.