{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:57Z","timestamp":1753893777320,"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 examine $n\\times n$ matrices over $Z_m$, with 0's in the diagonal and nonzeros elsewhere. If $m$ is a prime, then such matrices have large rank (i.e.,  $n^{1\/(p-1)}-O(1)$ ). If $m$ is a non-prime-power integer, then we show that  their rank can be much smaller. For $m=6$ we construct a matrix of rank $\\exp(c\\sqrt{\\log n\\log \\log n})$. We also show, that explicit constructions of such low rank matrices imply explicit constructions of Ramsey graphs.<\/jats:p>","DOI":"10.37236\/1493","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:05:12Z","timestamp":1578708312000},"source":"Crossref","is-referenced-by-count":10,"title":["Low Rank Co-Diagonal Matrices and Ramsey Graphs"],"prefix":"10.37236","volume":"7","author":[{"given":"Vince","family":"Grolmusz","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,3,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r15\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:24:44Z","timestamp":1579325084000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1493","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,3,12]]},"article-number":"R15"}}