{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822298,"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 explore an extremal hypergraph problem for which both the vertices and edges are ordered. Given a hypergraph $F$ (not necessarily simple), we consider\u00a0how many edges a simple hypergraph (no repeated edges) on $m$ vertices can have while forbidding $F$ as a subhypergraph where both hypergraphs have fixed vertex and edge orderings. A hypergraph of $n$ edges on $m$ vertices can be encoded as an $m\\times n$ (0,1)-matrix. We say a matrix is simple if it is a (0,1)-matrix with no repeated columns. Given a (0,1)-matrix $F$, we define ${\\hbox{fs}}(m,F)$ as the maximum, over all simple matrices $A$ which do not have $F$ as a submatrix, of the number of columns in $A$. The row and column order matter. It is known that if $F$ is $k\\times \\ell$ then ${\\hbox{fs}}(m,F)$\u00a0is $O(m^{2k-1-\\epsilon})$ where $\\epsilon=(k-1)\/(13\\log_2 \\ell)$. Anstee, Frankl, F\u00fcredi and Pach have conjectured that if $F$ is $k$-rowed, then \u00a0${\\hbox{fs}}(m,F)$ is $O(m^k)$. We show ${\\hbox{fs}}(m,F)$\u00a0is $O(m^2)$ for $F= \\left[{1\\,0\\,1\\,0\\,1\\atop 0\\,1\\,0\\,1\\,0}\\cdots\\right]$ and for $F= \\left[{1\\,0\\,1\\,0\\,1\\atop 1\\,0\\,1\\,0\\,1}\\cdots\\right]$. The proofs use a type of amortized analysis. We also give\u00a0some constructions.<\/jats:p>","DOI":"10.37236\/2166","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:50Z","timestamp":1578711650000},"source":"Crossref","is-referenced-by-count":1,"title":["Forbidden Submatrices: Some New Bounds and Constructions"],"prefix":"10.37236","volume":"20","author":[{"given":"R.P.","family":"Anstee","sequence":"first","affiliation":[]},{"given":"Ruiyuan","family":"Chen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:20:37Z","timestamp":1579299637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2166","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,14]]},"article-number":"P5"}}