Matthias Beck ; Yvonne Kemper - Flows on Simplicial Complexes

dmtcs:3085 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3085
Flows on Simplicial ComplexesArticle

Authors: Matthias Beck 1; Yvonne Kemper 2

  • 1 Department of Mathematics [San Francisco]
  • 2 Department of Mathematics [Univ California Davis]

Given a graph $G$, the number of nowhere-zero $\mathbb{Z}_q$-flows $\phi _G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\mathbb{Z} _q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: matroids, Tutte polynomial,Nowhere-zero flows, simplicial complexes,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • RUI: Computations in Ehrhart Theory; Funder: National Science Foundation; Code: 0810105
  • Algebraic and Geometric Computation with Applications; Funder: National Science Foundation; Code: 0914107
  • EMSW21-VIGRE: Focus on Mathematics; Funder: National Science Foundation; Code: 0636297

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