Federico Castillo ; Fu Liu - Ehrhart Positivity for Generalized Permutohedra

dmtcs:2505 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2505
Ehrhart Positivity for Generalized Permutohedra

Authors: Federico Castillo 1; Fu Liu 1

  • 1 University of California [Davis]

There are few general results about the coefficients of Ehrhart polynomials. We present a conjecture about their positivity for a certain family of polytopes known as generalized permutohedra. We have verified the conjecture for small dimensions combining perturbation methods with a new valuation on the algebra of rational pointed polyhedral cones constructed by Berline and Vergne.

https://doi.org/10.46298/dmtcs.2505
Source: HAL:hal-01337767v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: Ehrhart polynomials,Generalized permutohedra,Perturbations,Valuations,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Volumes, Ehrhart polynomials and valuations of polytopes; Funder: National Science Foundation; Code: 1265702

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