Federico Ardila ; Federico Castillo ; Michael Henley - 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) - https://doi.org/10.46298/dmtcs.2447
The arithmetic Tutte polynomials of the classical root systemsArticle

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 $A_n, B_n, C_n$, 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.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: Root systems,Toric arrangements,Tutte polynomials,Rogers-Ramanujan function,Signed graphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Creating Momentum through Communicating Mathematics; Funder: National Science Foundation; Code: 0841164
  • CAREER: Matroids, polytopes, and their valuations in algebra and geometry; Funder: National Science Foundation; Code: 0956178

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