{"paper":{"title":"Multivalued matrices and forbidden configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Attila Sali, Jeffrey Dawson, Linyuan Lu, Richard Anstee","submitted_at":"2017-10-01T16:19:24Z","abstract_excerpt":"An $r$-matrix is a matrix with symbols in $\\{0,1,\\ldots,r-1\\}$. A matrix is simple if it has no repeated columns. Let ${\\cal F}$ be a finite set of $r$-matrices. Let $\\hbox{forb}(m,r,{\\cal F})$ denote the maximum number of columns possible in a simple $r$-matrix\n  $A$ that has no submatrix which is a row and column permutation of any $F\\in{\\cal F}$. Many investigations have involved $r=2$. For general $r$, $\\hbox{forb}(m,r,{\\cal F})$ is polynomial in $m$ if and only if for every pair $i,j\\in\\{0,1,\\ldots,r-1\\}$ there is a matrix in ${\\cal F}$ whose entries are only $i$ or $j$.\n  Let ${\\cal T}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00374","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"}