{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:17Z","timestamp":1753893857283,"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>The present paper continues the work begun by Anstee, Ferguson, Griggs and Sali on small forbidden configurations. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. Let $F$ be a $k\\times l$ (0,1)-matrix (the forbidden configuration).  Assume $A$ is an $m\\times n$ simple matrix which has no submatrix which is a row and column permutation of $F$. We define ${\\hbox{forb}}(m,F)$ as the largest $n$, which would depend on $m$ and $F$, so that such an $A$ exists.  'Small' refers to the size of $k$ and in this paper $k=2$. For $p\\le q$, we set $F_{pq}$ to be the $2\\times (p+q)$ matrix with $p$ $\\bigl[{1\\atop0}\\bigr]$'s and $q$ $\\bigl[{0\\atop1}\\bigr]$'s. We give new exact values: ${\\hbox{forb}}(m,F_{0,4})=\\lfloor {5m\\over2}\\rfloor +2$, ${\\hbox{forb}}(m,F_{1,4})=\\lfloor {11m\\over4}\\rfloor +1$, ${\\hbox{forb}}(m,F_{1,5})=\\lfloor {15m\\over4}\\rfloor +1$, ${\\hbox{forb}}(m,F_{2,4})=\\lfloor {10m\\over3}-{4\\over3}\\rfloor$ and ${\\hbox{forb}}(m,F_{2,5})=4m$ (For ${\\hbox{forb}}(m,F_{1,4})$, ${\\hbox{forb}}(m,F_{1,5})$ we obtain equality only for certain classes modulo 4). In addition we provide a surprising construction which shows ${\\hbox{forb}}(m,F_{pq})\\ge \\bigl({p+q\\over2}+O(1)\\bigr)m$.<\/jats:p>","DOI":"10.37236\/997","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:47:41Z","timestamp":1578718061000},"source":"Crossref","is-referenced-by-count":2,"title":["Small Forbidden Configurations III"],"prefix":"10.37236","volume":"14","author":[{"given":"R. P.","family":"Anstee","sequence":"first","affiliation":[]},{"given":"N.","family":"Kamoosi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,11,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r79\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r79\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:59:26Z","timestamp":1579319966000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r79"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/997","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,11,12]]},"article-number":"R79"}}