{"paper":{"title":"The sorting index and set-valued joint equidistributions of $\\mathcal{B}_n$ and $\\mathcal{D}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sen-Peng Eu, Tsai-Lien Wong, Yuan-Hsun Lo","submitted_at":"2014-03-10T08:53:10Z","abstract_excerpt":"The sorting indices $\\text{sor}_B$ and $\\text{sor}_D$ on the Coxeter groups of type $B$ and $D$ respectively are defined by Petersen and it is proved that $(\\text{inv}_B, \\text{rlmin})$ and $(\\text{sor}_B, \\ell'_B)$ have the same joint distribution for type $B$ while $\\text{inv}_D$ and $\\text{sor}_D$ have the same distribution for type $D$. These results, including a set-valued extension of type $B$ involving two equildistributed pairs of three statistics, are proved combinatorially by Chen et al. via two mappings $\\varphi:=\\text{(B-code)}^{-1}\\circ \\text{(A-code)}$ and $\\psi:=\\text{(D-code)}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2169","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"}