{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:11:22Z","timestamp":1769584282777,"version":"3.49.0"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4666,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1994,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A partial Steiner (<jats:italic>n, k, l<\/jats:italic>)\u2010system or briefly (<jats:italic>n, k, l<\/jats:italic>)\u2010system is a pair (<jats:italic>V, S<\/jats:italic>), where <jats:italic>V<\/jats:italic> is an <jats:italic>n<\/jats:italic>\u2010set and <jats:italic>S<\/jats:italic> is a collection of <jats:italic>k<\/jats:italic>\u2010subsets of <jats:italic>V<\/jats:italic>, such that every <jats:italic>l<\/jats:italic>\u2010subset of <jats:italic>V<\/jats:italic> is contained in at most one <jats:italic>k<\/jats:italic>\u2010subset of S. A subset <jats:italic>X<\/jats:italic> \u2282 <jats:italic>V<\/jats:italic> is called independent if [<jats:italic>X<\/jats:italic>]<jats:sup><jats:italic>k<\/jats:italic><\/jats:sup> \u2229 S = 0. The size of the largest independent set in S is denoted by \u03b1(S). Define<\/jats:p><jats:p><jats:disp-formula>\n\n<\/jats:disp-formula>\n<\/jats:p><jats:p>The purpose of this note is to prove that for every <jats:italic>k, l, k<\/jats:italic> &gt; <jats:italic>l<\/jats:italic><\/jats:p><jats:p><jats:disp-formula>\n\n<\/jats:disp-formula>\nholds, where <jats:italic>c, d<\/jats:italic> are positive constants depending on <jats:italic>k<\/jats:italic> and <jats:italic>l<\/jats:italic> only.<\/jats:p>","DOI":"10.1002\/rsa.3240050117","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T13:56:35Z","timestamp":1180619795000},"page":"183-190","source":"Crossref","is-referenced-by-count":25,"title":["Note on independent sets in steiner systems"],"prefix":"10.1002","volume":"5","author":[{"given":"Vojt\u011bch","family":"R\u00f6dl","sequence":"first","affiliation":[]},{"given":"Edita","family":"\u0160inajov\u00e1","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(82)90049-8"},{"key":"e_1_2_1_3_2","unstructured":"N.Alon H.Lefmann andV.R\u00f6dl On an anti\u2010Ramsey type result (manuscript)."},{"key":"e_1_2_1_4_2","first-page":"242","article-title":"Coloring Steiner triple systems","volume":"3","author":"DeBrandes M.","year":"1982","journal-title":"SIAM J. Alg."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02020444"},{"key":"e_1_2_1_6_2","first-page":"609","volume-title":"Infinite and Finite Sets","author":"Erd\u00f6s P.","year":"1975"},{"key":"e_1_2_1_7_2","first-page":"2","article-title":"Maximal independent subsets in Steiner systems and planar sets","volume":"4","author":"Furedi Z.","year":"1991","journal-title":"SIAM J. Alg."},{"key":"e_1_2_1_8_2","unstructured":"R. L.GrahamandV.R\u00f6dl Numbers in Ramsey theory Surv. Combinat. (1987) London Math. Soc. Lect. Notes Ser. 123."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511566066"},{"key":"e_1_2_1_10_2","first-page":"167","article-title":"Steiner Triple systems with minimum independence number","volume":"21","author":"Phelps K. T.","year":"1986","journal-title":"Ars Combinat."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90044-9"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"R.Wilson An existence theory for pairwise balanced designs J. Combinat. Theory A 220\u2013245(1972).","DOI":"10.1016\/0097-3165(72)90028-3"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240050117","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240050117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,15]],"date-time":"2023-10-15T22:29:54Z","timestamp":1697408994000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240050117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/rsa.3240050117"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240050117","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}