{"paper":{"title":"Major index distribution over permutation classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michal Opler","submitted_at":"2015-05-26T21:06:20Z","abstract_excerpt":"For a permutation $\\pi$ the major index of $\\pi$ is the sum of all indices $i$ such that $\\pi_i > \\pi_{i+1}$. It is well known that the major index is equidistributed with the number of inversions over all permutations of length $n$. In this paper, we study the distribution of the major index over pattern-avoiding permutations of length $n$. We focus on the number $M_n^m(\\Pi)$ of permutations of length $n$ with major index $m$ and avoiding the set of patterns $\\Pi$.\n  First we are able to show that for a singleton set $\\Pi = \\{\\sigma\\}$ other than some trivial cases, the values $M_n^m(\\Pi)$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07135","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"}