On permutation polytopes

Details On permutation polytopes On permutation polytopes

2007-09-11

arxiv.org/abs/0709.1615v1

Adv. Math. 222 (2009), 431-452

Mathematics

Combinatorics

AMS-LaTeX, 22 pages

Scientific paper

A permutation polytope is the convex hull of a group of permutation matrices. In this paper we investigate the combinatorics of permutation polytopes and their faces. As applications we completely classify permutation polytopes in dimensions 2,3,4, and the corresponding permutation groups up to a suitable notion of equivalence. We also provide a list of combinatorial types of possibly occuring faces of permutation polytopes up to dimension four.

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