{"paper":{"title":"Excess Coverage Arrays and Levenshtein's Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amber E. Gentle, Daniel Horsley, Ian M. Wanless","submitted_at":"2024-11-26T06:28:11Z","abstract_excerpt":"A sequence covering array, denoted \\textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\\{0, \\dots, v-1 \\}$ such that each sequence of $t$ distinct elements of $\\{0, \\dots, v-1\\}$ reads left to right in at least one permutation. The minimum number of permutations such a sequence covering array can have is $t!$ and Levenshtein conjectured that if a sequence covering array with $t!$ permutations exists, then $v \\in \\{t,t+1\\}$. In this paper, we prove that if an \\textsf{SCA}$(7!;7,v)$ exists, then $v \\leq 9$. We do this by analysing connections between sequence covering arrays and a special ki"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17145","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/2411.17145/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"}