{"paper":{"title":"Jumbled Scattered Factors","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Annika Huch, Melf Kammholz, Pamela Fleischmann, Tore Ko{\\ss}","submitted_at":"2025-06-04T10:37:22Z","abstract_excerpt":"In this work, we combine the research on (absent) scattered factors with the one of jumbled words. For instance, $\\mathtt{wolf}$ is an absent scattered factor of $\\mathtt{cauliflower}$ but since $\\mathtt{lfow}$, a jumbled (or abelian) version of $\\mathtt{wolf}$, is a scattered factor, $\\mathtt{wolf}$ occurs as a jumbled scattered factor in $\\mathtt{cauliflower}$. A \\emph{jumbled scattered factor} $u$ of a word $w$ is constructed by letters of $w$ with the only rule that the number of occurrences per letter in $u$ is smaller than or equal to the one in $w$. We proceed to partition and character"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03814","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03814/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}