{"paper":{"title":"Proof of a conjecture of Kl{\\o}ve on permutation codes under the Chebychev distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Victor J. W. Guo, Yiting Yang","submitted_at":"2017-04-05T07:52:18Z","abstract_excerpt":"Let $d$ be a positive integer and $x$ a real number. Let $A_{d, x}$ be a $d\\times 2d$ matrix with its entries $$ a_{i,j}=\\left\\{ \\begin{array}{ll} x\\ \\ & \\mbox{for} \\ 1\\leqslant j\\leqslant d+1-i, 1\\ \\ & \\mbox{for} \\ d+2-i\\leqslant j\\leqslant d+i, 0\\ \\ & \\mbox{for} \\ d+1+i\\leqslant j\\leqslant 2d. \\end{array} \\right. $$ Further, let $R_d$ be a set of sequences of integers as follows: $$R_d=\\{(\\rho_1, \\rho_2,\\ldots, \\rho_d)|1\\leqslant \\rho_i\\leqslant d+i, 1\\leqslant i \\leqslant d,\\ \\mbox{and}\\ \\rho_r\\neq \\rho_s\\ \\mbox{for}\\ r\\neq s\\}.$$ and define $$\\Omega_d(x)=\\sum_{\\rho\\in R_d}a_{1,\\rho_1}a_{2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01295","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":""},"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"}