Geodesic
The arithmetic Tutte polynomials of the classical root systems
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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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 <i>arithmetic</i> 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. 
@article{DMTCS_2014_special_265_a72,
     author = {Ardila, Federico and Castillo, Federico and Henley, Michael},
     title = {The arithmetic {Tutte} polynomials of the classical root systems},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2447},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2447/}
}
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AU  - Henley, Michael
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%A Castillo, Federico
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%T The arithmetic Tutte polynomials of the classical root systems
%J Discrete mathematics & theoretical computer science
%D 2014
%V DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
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Ardila, Federico; Castillo, Federico; Henley, Michael. The arithmetic Tutte polynomials of the classical root systems. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2447. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2447/

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