{"paper":{"title":"Fast Computation of Abelian Runs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arnaud Lefebvre, Elise Prieur-Gaston, Gabriele Fici, Thierry Lecroq, Tomasz Kociumaka","submitted_at":"2015-06-29T06:24:08Z","abstract_excerpt":"Given a word $w$ and a Parikh vector $\\mathcal{P}$, an abelian run of period $\\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\\sigma$ and a Parikh vector $\\mathcal{P}$, returns all the abelian runs of period $\\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\\sigma+p)$, where $p$ is the norm of $\\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08518","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"}