{"paper":{"title":"Pattern-Avoiding Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Bruce Sagan, Robert Davis","submitted_at":"2016-09-06T22:50:54Z","abstract_excerpt":"Two well-known polytopes whose vertices are indexed by permutations in the symmetric group $\\mathfrak{S}_n$ are the permutohedron $P_n$ and the Birkhoff polytope $B_n$. We consider polytopes $P_n(\\Pi)$ and $B_n(\\Pi)$, whose vertices correspond to the permutations in $\\mathfrak{S}_n$ avoiding a set of patterns $\\Pi$. For various choices of $\\Pi$, we explore the Ehrhart polynomials and $h^*$-vectors of these polytopes as well as other aspects of their combinatorial structure.\n  For $P_n(\\Pi)$, we consider all subsets $\\Pi \\subseteq \\mathfrak{S}_3$ and are able to provide results in most cases. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01782","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}