{"paper":{"title":"New Lower Bounds for Permutation Arrays Using Contraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"I.H. Sudborough, Linda Morales, Luis Gerardo Mojica, Sergey Bereg, Zevi Miller","submitted_at":"2018-04-11T01:02:32Z","abstract_excerpt":"A permutation array $A$ is a set of permutations on a finite set $\\Omega$, say of size $n$. Given distinct permutations $\\pi, \\sigma\\in \\Omega$, we let $hd(\\pi, \\sigma) = |\\{ x\\in \\Omega: \\pi(x) \\ne \\sigma(x) \\}|$, called the Hamming distance between $\\pi$ and $\\sigma$. Now let $hd(A) =$ min$\\{ hd(\\pi, \\sigma): \\pi, \\sigma \\in A \\}$. For positive integers $n$ and $d$ with $d\\le n$, we let $M(n,d)$ be the maximum number of permutations in any array $A$ satisfying $hd(A) \\geq d$. There is an extensive literature on the function $M(n,d)$, motivated in part by suggested applications to error corre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03768","kind":"arxiv","version":3},"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"}