{"paper":{"title":"On a refinement of Wilf-equivalence for permutations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huiyun Ge, Sherry H.F. Yan, Yaqiu Zhang","submitted_at":"2014-10-11T00:52:45Z","abstract_excerpt":"Recently, Dokos et al. conjectured that for all $k, m\\geq 1$, the patterns $ 12\\ldots k(k+m+1)\\ldots (k+2)(k+1) $ and $(m+1)(m+2)\\ldots (k+m+1)m\\ldots 21 $ are $maj$-Wilf-equivalent. In this paper, we confirm this conjecture for all $k\\geq 1$ and $m=1$. In fact, we construct a descent set preserving bijection between $ 12\\ldots k (k-1) $-avoiding permutations and $23\\ldots k1$-avoiding permutations for all $k\\geq 3$. As a corollary, our bijection enables us to settle a conjecture of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2933","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"}