The arithmetic Tutte polynomials of the classical root systems

Federico Ardila 1, 2 Federico Castillo 2, 3 Michael Henley 4
1 San Francisco State University - Department of Mathematics
2 Universidad de los Andes [Bogota]
3 University of California [Davis]
4 SFSU - San Francisco State University
Abstract : 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 : Root systems Toric arrangements Tutte polynomials Rogers-Ramanujan function Signed graphs
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Communication dans un congrès
Louis J. Billera and Isabella Novik. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), pp.851-862, 2014, DMTCS Proceedings
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Federico Ardila, Federico Castillo, Michael Henley. The arithmetic Tutte polynomials of the classical root systems. Louis J. Billera and Isabella Novik. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), pp.851-862, 2014, DMTCS Proceedings. 〈hal-01207564〉

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