Discrete Mathematics & Theoretical Computer Science |

- 1 Department of Mathematics [San Francisco]
- 2 Universidad de los Andes [Bogota]
- 3 Universidad de los Andes [Bogota]
- 4 University of California [Davis]
- 5 San Francisco State University

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.

Source: HAL:hal-01207564v1

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
*CAREER: Matroids, polytopes, and their valuations in algebra and geometry*; Funder: National Science Foundation; Code: 0956178*Creating Momentum through Communicating Mathematics*; Funder: National Science Foundation; Code: 0841164

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