{"paper":{"title":"Graphical Mahonian Statistics on Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amy Grady, Svetlana Poznanovi\\'c","submitted_at":"2016-06-30T20:39:31Z","abstract_excerpt":"Foata and Zeilberger defined the graphical major index, $\\mathrm{maj}'_U$, and the graphical inversion index, $\\mathrm{inv}'_U$, for words. These statistics are a generalization of the classical permutation statistics $\\mathrm{maj}$ and $\\mathrm{inv}$ indexed by directed graphs $U$. They showed that $\\mathrm{maj}'_U$ and $\\mathrm{inv}'_U$ are equidistributed over all rearrangement classes if and only if $U$ is bipartitional. In this paper we strengthen their result by showing that if $\\mathrm{maj}'_U$ and $\\mathrm{inv}'_U$ are equidistributed on a single rearrangement class then $U$ is essenti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00033","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"}