Permutation polytopes and indecomposable elements in permutation groups
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Each group G of nxn permutation matrices has a corresponding permutation polytope, P(G):=conv(G) in R^{nxn}. We relate the structure of P(G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t,floor(n/2)} is a sharp upper bound on the diameter of the graph of P(G); so if G is transitive, the diameter is at most 2. We also show that P(G) achieves its maximal dimension of (n-1)^2 precisely when G is 2-transitive. We then extend results of I. Pak on mixing times for a random walk on P(G). Our work depends on a new result for permutation groups involving writing permutations as products of indecomposable permutations.
18 pages. To appear in the Journal of Combinatorial Theory, Series A. A corollary about solvable primitive permutation groups has been added. We have fixed some typos and made revisions according to referees' comments
18 pages. To appear in the Journal of Combinatorial Theory, Series A. A corollary about solvable primitive permutation groups has been added. We have fixed some typos and made revisions according to referees' comments