English

Permutation Polytopes of Cyclic Groups

Combinatorics 2011-09-02 v1 Group Theory

Abstract

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. We give formulas for their dimension and vertex degree. 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.

Keywords

Cite

@article{arxiv.1109.0191,
  title  = {Permutation Polytopes of Cyclic Groups},
  author = {Barbara Baumeister and Christian Haase and Benjamin Nill and Andreas Paffenholz},
  journal= {arXiv preprint arXiv:1109.0191},
  year   = {2011}
}

Comments

15 pages

R2 v1 2026-06-21T18:58:23.239Z