{"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). In 2012, Billey, Burdzy and Sagan investigated the analogous problem for permutations in the symmetric group,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6621","kind":"arxiv","version":1},"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"}