{"paper":{"title":"On the Fixed-Length-Burst Levenshtein Ball with Unit Radius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Gennian Ge, Yuanxiao Xi, Yubo Sun","submitted_at":"2025-06-09T14:45:36Z","abstract_excerpt":"Consider a length-$n$ sequence $\\bm{x}$ over a $q$-ary alphabet. The \\emph{fixed-length Levenshtein ball} $\\mathcal{L}_t(\\bm{x})$ of radius $t$ encompasses all length-$n$ $q$-ary sequences that can be derived from $\\bm{x}$ by performing $t$ deletions followed by $t$ insertions. Analyzing the size and structure of these balls presents significant challenges in combinatorial coding theory. Recent studies have successfully characterized fixed-length Levenshtein balls in the context of a single deletion and a single insertion. These works have derived explicit formulas for various key metrics, inc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07817","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/2506.07817/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"}