Face-subgroups of permutation polytopes

TL;DR

This paper proves a conjecture regarding the characterization of subgroups of permutation groups whose associated permutation polytopes form faces of larger permutation polytopes, simplifying previous complex proofs.

Contribution

It provides a straightforward proof of a conjecture about when permutation polytopes of subgroups are faces of larger permutation polytopes.

Findings

Confirmed the conjecture with a simple proof

Characterized subgroup conditions for face inclusion

Simplified understanding of permutation polytope faces

Abstract

In [Baumeister, H., Nill, Paffenholz, On permutation polytopes, Adv. Math. 222 (2009), 431-452 / arXiv:0709.1615] we conjectured a characterization of subgroups H of a permutation group G so that, on the level of permutation polytopes, P(H) is a face of P(G). Here we present the embarrassingly simple proof of this conjecture.