Geodesic
Permutation Polytopes of Cyclic Groups
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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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. 
@article{DMTCS_2012_special_263_a37,
     author = {Baumeister, Barbara and Haase, Christian and Nill, Benjamin and Paffenholz, Andreas},
     title = {Permutation {Polytopes} of {Cyclic} {Groups}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3051/}
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Baumeister, Barbara; Haase, Christian; Nill, Benjamin; Paffenholz, Andreas. Permutation Polytopes of Cyclic Groups. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3051. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3051/

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