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The arithmetic Tutte polynomials of the classical root systems

Authors
  • Ardila, Federico
  • Castillo, Federico
  • Henley, Michael
Publication Date
Jan 01, 2014
Source
HAL-SHS
Keywords
Language
English
License
Unknown
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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 <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.

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