{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:04:21Z","timestamp":1758823461542,"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 give a generalization for the Deza-Frankl-Singhi Theorem in case of multiple intersections.  More exactly, we prove, that if ${\\cal H}$  is a set-system, which satisfies that for some $k$, the $k$-wise intersections occupy only $\\ell$ residue-classes modulo a $p$ prime, while the sizes of the members of ${\\cal H}$ are not in these residue classes, then the size of ${\\cal H}$ is at most $$(k-1)\\sum_{i=0}^{\\ell}{n\\choose i}$$ This result considerably strengthens an upper bound of F\u00fcredi (1983), and gives partial answer to a question of T. S\u00f3s (1976). As an application, we give a direct, explicit construction for coloring the $k$-subsets of an $n$ element set with $t$ colors, such that no monochromatic complete hypergraph on $$\\exp{(c(\\log m)^{1\/t}(\\log \\log m)^{1\/(t-1)})}$$ vertices exists.<\/jats:p>","DOI":"10.37236\/1625","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:27:19Z","timestamp":1578709639000},"source":"Crossref","is-referenced-by-count":5,"title":["Set-Systems with Restricted Multiple Intersections"],"prefix":"10.37236","volume":"9","author":[{"given":"Vince","family":"Grolmusz","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,2,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:15:29Z","timestamp":1579324529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1625","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,2,20]]},"article-number":"R8"}}