Baumeister, Barbara and Haase, Christian and Nill, Benjamin and Paffenholz, Andreas - 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)
Permutation Polytopes of Cyclic Groups

Authors: Baumeister, Barbara and Haase, Christian and Nill, Benjamin and Paffenholz, Andreas

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
Submitted 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]


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