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An index i is a peak of \\pi if \\pi_{i-1}<\\pi_i>\\pi_{i+1} and P_B(\\pi) denotes the set of all peaks of \\pi. Given any set S, we define P_B(S,n) to be the set of signed permutations \\pi \\in B_n with P_B(\\pi) = S. In this paper we are interested in the cardinality of the set P_B(S,n). In 2012, Billey, Burdzy and Sagan investigated the analogous problem for permutations in the symmetric group,"},"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":"1308.6621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-29T22:57:32Z","cross_cats_sorted":[],"title_canon_sha256":"de0d5a4ec51b8c75940c826bb420a215b8a128c2f0d9b82b9945556499bd3d8f","abstract_canon_sha256":"accbd592b00064e9707bf02ce669deb8771644e434e6fe472ae90b705abf3efb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:38.625644Z","signature_b64":"9+YLdPtML+h70l+/E5CDljdMd6t4wmqjoYM46wQVA3gF0gnhHMZuftyxwjNyALUPLSRFVuBKiqBXgkkZaCIZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a771f0d75cd09cf45e73595461ab1e8dbfc63d8a271ffda200c8c61452ab89ae","last_reissued_at":"2026-05-18T03:14:38.625016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:38.625016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Number of permutations with same peak set for signed permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Diaz-Lopez, Francis Castro-Velez, Jose Pastrana, Rita Zevallos, Rosa Orellana","submitted_at":"2013-08-29T22:57:32Z","abstract_excerpt":"A signed permutation \\pi = \\pi_1\\pi_2 \\ldots \\pi_n in the hyperoctahedral group B_n is a word such that each \\pi_i \\in {-n, \\ldots, -1, 1, \\ldots, n} and {|\\pi_1|, |\\pi_2|, \\ldots, |\\pi_n|} = {1,2,\\ldots,n}. An index i is a peak of \\pi if \\pi_{i-1}<\\pi_i>\\pi_{i+1} and P_B(\\pi) denotes the set of all peaks of \\pi. Given any set S, we define P_B(S,n) to be the set of signed permutations \\pi \\in B_n with P_B(\\pi) = S. In this paper we are interested in the cardinality of the set P_B(S,n). 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