{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:37Z","timestamp":1753893817798,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the following extremal set theory problem. Define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. An $m$-rowed simple matrix corresponds to a family of subsets of $\\{1,2,\\ldots ,m\\}$. Let $m$ be a given integer and $F$ be a given (0,1)-matrix (not necessarily simple). We say a matrix $A$ has $F$ as a configuration if a submatrix of $A$ is a row and column permutation of $F$. We define $\\hbox{forb}(m,F)$ as the maximum number of columns that a simple $m$-rowed matrix $A$ can have subject to the condition that $A$ has no configuration $F$. We compute exact values for $\\hbox{forb}(m,F)$ for some choices of $F$ and in doing so handle all $3\\times 3$ and some $k\\times 2$ (0,1)-matrices $F$. Often $\\hbox{forb}(m,F)$ is determined by $\\hbox{forb}(m,F')$ for some configuration $F'$ contained in $F$ and in that situation, with $F'$ being minimal, we call $F'$ a critical substructure.<\/jats:p>","DOI":"10.37236\/322","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:14:48Z","timestamp":1578716088000},"source":"Crossref","is-referenced-by-count":1,"title":["Forbidden Configurations: Exact Bounds Determined by Critical Substructures"],"prefix":"10.37236","volume":"17","author":[{"given":"R. P.","family":"Anstee","sequence":"first","affiliation":[]},{"given":"S. N.","family":"Karp","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,3,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:57:17Z","timestamp":1579305437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/322","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,3,29]]},"article-number":"R50"}}