Geodesic
Pattern-Avoiding Polytopes
Séminaire lotharingien de combinatoire, 78B (2017)
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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. 

@article{SLC_2017_78B_a1,
     author = {Robert Davis and Bruce Sagan},
     title = {Pattern-Avoiding {Polytopes}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a1/}
}
TY  - JOUR
AU  - Robert Davis
AU  - Bruce Sagan
TI  - Pattern-Avoiding Polytopes
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a1/
ID  - SLC_2017_78B_a1
ER  - 
%0 Journal Article
%A Robert Davis
%A Bruce Sagan
%T Pattern-Avoiding Polytopes
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a1/
%F SLC_2017_78B_a1
Robert Davis; Bruce Sagan. Pattern-Avoiding Polytopes. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a1/