{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:01Z","timestamp":1753893781433,"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, Griggs and Sali on small forbidden configurations. In the notation of (0,1)-matrices, we consider a (0,1)-matrix $F$ (the forbidden configuration), an $m\\times n$ (0,1)-matrix $A$ with no repeated columns which has no submatrix which is a row and column permutation of $F$, and seek bounds on $n$ in terms of $m$ and $F$. We give new exact bounds for some  $2\\times l$ forbidden configurations and some asymptotically exact bounds for some other $2\\times l$ forbidden configurations. We frequently employ graph theory and in one case develop a new vertex ordering for directed graphs that generalizes R\u00e9dei's Theorem for Tournaments. One can now imagine that exact bounds could be available for all $2\\times l$ forbidden configurations. Some progress is reported for $3\\times l$ forbidden configurations. These bounds are improvements of the general bounds obtained by Sauer, Perles and Shelah, Vapnik and Chervonenkis. <\/jats:p>","DOI":"10.37236\/1548","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:49Z","timestamp":1578708589000},"source":"Crossref","is-referenced-by-count":4,"title":["Small Forbidden Configurations II"],"prefix":"10.37236","volume":"8","author":[{"given":"Richard","family":"Anstee","sequence":"first","affiliation":[]},{"given":"Ron","family":"Ferguson","sequence":"additional","affiliation":[]},{"given":"Attila","family":"Sali","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,10,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:21:44Z","timestamp":1579324904000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,10,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1548","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,10,3]]},"article-number":"R4"}}