{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821086,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $t\\ge 1$ be a given integer. Let ${\\cal F}$ be a family of subsets of $[m]=\\{1,2,\\ldots ,m\\}$. Assume that for every pair of disjoint sets $S,T\\subset [m]$ with $|S|=|T|=k$, there do not exist $2t$ sets in ${\\cal F}$ where $t$ subsets of ${\\cal F}$ contain $S$ and are disjoint from $T$ and $t$ subsets of ${\\cal F}$ contain $T$ and are disjoint from $S$. We show that $|{\\cal F}|$ is $O(m^{k})$. Our main new ingredient is allowing, during the inductive proof, multisets of subsets of $[m]$ where the multiplicity of a given set is bounded by $t-1$. We use a strong stability result of Anstee and Keevash. This is further evidence for a conjecture of Anstee and Sali. These problems can be stated in the language of matrices. Let $t\\cdot M$ denote $t$ copies of the matrix $M$ concatenated together. We have established the conjecture for those configurations $t\\cdot F$ for any $k\\times 2$ (0,1)-matrix $F$.<\/jats:p>","DOI":"10.37236\/3345","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:21:22Z","timestamp":1578687682000},"source":"Crossref","is-referenced-by-count":0,"title":["Repeated Columns and an Old Chestnut"],"prefix":"10.37236","volume":"20","author":[{"given":"R. P.","family":"Anstee","sequence":"first","affiliation":[]},{"given":"Linyuan","family":"Lu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,10,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:12:10Z","timestamp":1579241530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,14]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3345","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,10,14]]},"article-number":"P2"}}