Barbara Baumeister ; Christian Haase ; Benjamin Nill ; Andreas Paffenholz - Permutation Polytopes of Cyclic Groups

dmtcs:3051 - 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.3051
Permutation Polytopes of Cyclic Groups

Authors: Barbara Baumeister ; Christian Haase ; Benjamin Nill ; Andreas Paffenholz ORCID-iD

    We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is already quite complex. For a large class of examples we show that there exist exponentially many facets.


    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: permutation groups, cyclic groups, convex polytopes, 0/1-polytopes, marginal polytopes,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Lattice Polytopes with a View Toward Algebraic Geometry; Funder: National Science Foundation; Code: 1102424
    • Lattice Polytopes with a View Toward Algebraic Geometry; Funder: National Science Foundation; Code: 1203162

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