{"paper":{"title":"Modified Growth Diagrams, Permutation Pivots, and the BXW map $\\phi^*$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Saracino, Jonathan Bloom","submitted_at":"2011-03-02T00:03:56Z","abstract_excerpt":"In their paper [1] on Wilf-equivalence for singleton classes, Backelin, Xin, and West introduce a transformation $\\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. In [3], Bousquet-M$\\acute{\\textrm{e}}$lou and Steingr$\\acute{\\textrm{\\i}}$msson prove the analogue of the main result of [1] in the context of involutions, and in so doing they must prove that $\\phi^*$ commutes with the operation of taking inverses. The proof of this commutation result is long and difficult, and Bousquet-M$\\acute{\\textrm{e}}$lou and Steingr$\\acute{\\textrm{\\i}}$ms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0319","kind":"arxiv","version":2},"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"}