{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:53:39Z","timestamp":1774626819777,"version":"3.50.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2012,10,11]],"date-time":"2012-10-11T00:00:00Z","timestamp":1349913600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is<jats:italic>j-independent<\/jats:italic>if its intersection with any edge has size strictly less than<jats:italic>j<\/jats:italic>. The Kruskal\u2013Katona theorem implies that in an<jats:italic>r<\/jats:italic>-uniform hypergraph with a fixed size and order, the hypergraph with the most<jats:italic>r<\/jats:italic>-independent sets is the lexicographic hypergraph. In this paper, we use a hypergraph regularity lemma, along with a technique developed by Loh, Pikhurko and Sudakov, to give an asymptotically best possible upper bound on the number of<jats:italic>j<\/jats:italic>-independent sets in an<jats:italic>r<\/jats:italic>-uniform hypergraph.<\/jats:p>","DOI":"10.1017\/s0963548312000454","type":"journal-article","created":{"date-parts":[[2012,10,11]],"date-time":"2012-10-11T14:48:17Z","timestamp":1349966897000},"page":"9-20","source":"Crossref","is-referenced-by-count":8,"title":["Hypergraph Independent Sets"],"prefix":"10.1017","volume":"22","author":[{"given":"JONATHAN","family":"CUTLER","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. 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