{"paper":{"title":"On Two Bijections from S_n(321) to S_n(132)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Saracino","submitted_at":"2010-08-26T17:53:48Z","abstract_excerpt":"Let S_n(321) (respectively, S_n(132)) denote the set of all permutations of {1,2,...,n} that avoid the pattern 321 (respectively, the pattern 132). Elizalde and Pak gave a bijection Theta from S_n(321) to S_n(132) that preserves the numbers of fixed points and excedances for each element of S_n(321), and commutes with the operation of taking inverses. Bloom and Saracino proved that another bijection Gamma from S_n(321) to S_n(132), introduced by Robertson, has the same properties, and they later gave a pictorial reformulation of Gamma that made these results more transparent. Here we give a pi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4557","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"}