{"paper":{"title":"Peaks Sets of Classical Coxeter Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Diaz-Lopez, Darleen Perez-Lavin, Erik Insko, Pamela E. Harris","submitted_at":"2015-05-18T00:21:09Z","abstract_excerpt":"We say a permutation $\\pi=\\pi_1\\pi_2\\cdots\\pi_n$ in the symmetric group $\\mathfrak{S}_n$ has a peak at index $i$ if $\\pi_{i-1}<\\pi_i>\\pi_{i+1}$ and we let $P(\\pi)=\\{i \\in \\{1, 2, \\ldots, n\\} \\, \\vert \\, \\mbox{$i$ is a peak of $\\pi$}\\}$. Given a set $S$ of positive integers, we let $P (S; n)$ denote the subset of $\\mathfrak{S}_n$ consisting of all permutations $\\pi$, where $P(\\pi) =S$. In 2013, Billey, Burdzy, and Sagan proved $|P(S;n)| = p(n)2^{n-\\lvert S\\rvert-1}$, where $p(n)$ is a polynomial of degree $\\max(S)- 1$. In 2014, Castro-Velez et al. considered the Coxeter group of type $B_n$ as t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04479","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"}