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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.04479","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-18T00:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"bfcac5d117fc7a8a159d1e7b3f23f1937c2b7beca2855812acf9886d792e0a73","abstract_canon_sha256":"d82b542e029f6bced5aec09b66f4e3e19e3af878e70d2a196ca8ca982440f8bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:18.494205Z","signature_b64":"2UPHALteP6VIJ9R/4FrbTeVFjthCAZPWi0NweJDyi+ICOZe+AOwCV+rRPGInHhxvFqo7vmyoraRdyKwCoT1mDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"670dcea2787eca52f49961b5451cda02f56df777c499f9640f05833e6180ff99","last_reissued_at":"2026-05-18T00:57:18.493719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:18.493719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\max(S)- 1$. 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