{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835762,"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 polynomial upper bound on the size of set systems with restricted $t$-wise intersections modulo prime powers.  Let $t\\geq 2$. Let $p$ be a prime and $q=p^{\\alpha}$ be a prime power. Let ${\\cal L}=\\{l_1,l_2,\\ldots,l_s\\}$ be a subset of $\\{0, 1, 2, \\ldots, q-1\\}$. If ${\\cal F}$ is a family of subsets of an $n$ element set $X$ such that $|F_{1}\\cap \\cdots \\cap F_{t}| \\pmod{q} \\in {\\cal L}$ for any collection of $t$ distinct sets from ${\\cal F}$ and $|F| \\pmod{q} \\notin {\\cal L}$ for every $F\\in {\\cal F}$, then $$ |{\\cal F}|\\leq {t(t-1)\\over2}\\sum_{i=0}^{2^{s-1}}{n\\choose i}. $$ Our result extends a theorem of  Babai, Frankl, Kutin, and \u0160tefankovi\u010d, who studied the $2$-wise case for prime power moduli, and also complements a result of Grolmusz that no polynomial upper bound holds for non-prime-power composite moduli.<\/jats:p>","DOI":"10.37236\/255","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:29:20Z","timestamp":1578716960000},"source":"Crossref","is-referenced-by-count":0,"title":["Set Systems with Restricted $t$-wise Intersections Modulo Prime Powers"],"prefix":"10.37236","volume":"16","author":[{"given":"Rudy X. J.","family":"Liu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,6,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:53:05Z","timestamp":1579315985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/255","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,6,5]]},"article-number":"N17"}}