{"paper":{"title":"The sorting index on colored permutations and even-signed permutations","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":"2014-09-29T12:12:24Z","abstract_excerpt":"We define a new statistic $\\mathsf{sor}$ on the set of colored permutations $\\mathsf{G}_{r,n}$ and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of $n$ non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: $(\\ell,\\mathsf{Rmil}^0,\\mathsf{Rmil}^1,...,\\mathsf{Rmil}^{r-1}$, $\\mathsf{Lmil}^0,\\mathsf{Lmil}^1,...,\\mathsf{Lmil}^{r-1}$, $\\mathsf{Lmal}^0,\\mathsf{Lmal}^1,...,\\mathsf{Lmal}^{r-1}$, $\\mathsf{Lmap}^0,\\mathsf{Lma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8093","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"}