{"paper":{"title":"Avoiding patterns in matrices via a small number of changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Axenovich, Ryan R. Martin","submitted_at":"2016-05-21T02:50:35Z","abstract_excerpt":"Let ${\\cal A}=\\{A_1,\\ldots, A_r\\}$ be a partition of a set $\\{1,\\ldots,m\\}\\times\\{1,\\ldots, n\\}$ into $r$ nonempty subsets, and $A=(a_{ij})$ be an $m\\times n$ matrix. We say that $A$ has a pattern ${\\cal A}$ provided that $a_{ij}=a_{i'j'}$ if and only if $(i,j),(i',j')\\in A_t$ for some $t\\in\\{1,\\ldots,r\\}$. In this note we study the following function $f$ defined on the set of all $m\\times n$ matrices $M$ with $s$ distinct entries: $f(M; {\\cal A})$ is the smallest number of positions where the entries of $M$ need to be changed such that the resulting matrix does not have any submatrix with pat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06577","kind":"arxiv","version":2},"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"}