{"paper":{"title":"Generating functions for descents over permutations which avoid sets of consecutive patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeffrey B. Remmel, Quang T. Bach","submitted_at":"2015-10-14T21:12:55Z","abstract_excerpt":"We extend the reciprocity method of Jones and Remmel to study generating functions of the form $$\\sum_{n \\geq 0} \\frac{t^n}{n!} \\sum_{\\sigma \\in \\mathcal{NM}_n(\\Gamma)}x^{\\mathrm{LRmin}(\\sigma)}y^{1+\\mathrm{des}(\\sigma)}$$ where $\\Gamma$ is a set of permutations which start with 1 and have at most one descent, $\\mathcal{NM}_n(\\Gamma)$ is the set of permutations $\\sigma$ in the symmetric group $\\mathfrak{S}_n$ which have no $\\Gamma$-matches, $\\mathrm{des}(\\sigma)$ is the number of descents of $\\sigma$ and $\\mathrm{LRmin}(\\sigma)$ is the number of left-to-right minima of $\\sigma$. We show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04319","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"}