{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T13:29:04Z","timestamp":1762608544188},"reference-count":25,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T00:00:00Z","timestamp":1639440000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2022,10]]},"abstract":"Abstract<\/jats:title>A k<\/jats:italic>\u2010uniform hypergraph with n<\/jats:italic> vertices is an \u2010omitting system if it has no two edges with intersection size . If in addition it has no two edges with intersection size greater than , then it is an \u2010system. R\u00f6dl and \u0160i\u0148ajov\u00e1 proved a sharp lower bound for the independence number of \u2010systems. We consider the same question for \u2010omitting systems. Our proofs use adaptations of the random greedy independent set algorithm, and pseudorandom graphs. We also prove related results where we forbid more than two edges with a prescribed common intersection size leading to some applications in Ramsey theory. For example, we obtain good bounds for the Ramsey number , where F<\/jats:italic> is the k<\/jats:italic>\u2010uniform Fan. The behavior is quite different than the case which is the classical Ramsey number .<\/jats:p>","DOI":"10.1002\/rsa.21071","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T10:04:00Z","timestamp":1639476240000},"page":"493-519","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Independent sets in hypergraphs omitting an intersection"],"prefix":"10.1002","volume":"61","author":[{"given":"Tom","family":"Bohman","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences Carnegie Mellon University Pittsburgh Pennsylvania USA"}]},{"given":"Xizhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science University of Illinois Chicago Chicago Illinois USA"}]},{"given":"Dhruv","family":"Mubayi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science University of Illinois Chicago Chicago Illinois USA"}]}],"member":"311","published-online":{"date-parts":[[2021,12,14]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579451"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(82)90049-8"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(80)90030-8"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-011-9555-4"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20667"},{"key":"e_1_2_7_7_1","first-page":"3","article-title":"Teoria statistica delle classi e calcolo delle probabilita","volume":"8","author":"Bonferroni C.","year":"1936","journal-title":"Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commericiali di Firenze"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-014-3219-8"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-36.2.369"},{"key":"e_1_2_7_10_1","doi-asserted-by":"crossref","unstructured":"R. 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