Séminaire Lotharingien de Combinatoire, 78B.2 (2017), 12 pp.
Robert Davis and Bruce Sagan
The Birkhoff polytope is a long-studied polytope connected to many
areas of mathematics. In this paper, we generalize it by considering
convex hulls of subsets of its vertices. The vertices chosen
correspond to avoidance classes of permutations. We study the
structure of two special cases, leading to connections with shellable
order complexes, toric ideals, standard Young tableaux, and
(P,ω)-partitions. We also find that these polytopes have
palindromic and unimodal h*-vectors.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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