乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T09:10:46Z","timestamp":1665997846834},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,5,1]],"date-time":"2009-05-01T00:00:00Z","timestamp":1241136000000},"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":[[2009,5]]},"abstract":"A d<\/jats:italic>-simplex is a collection of d<\/jats:italic> + 1 sets such that every d<\/jats:italic> of them has non-empty intersection and the intersection of all of them is empty. Fix k<\/jats:italic> \u2265 d<\/jats:italic> + 2 \u2265 3 and let

<\/jats:private-char> be a family of k<\/jats:italic>-element subsets of an n<\/jats:italic>-element set that contains no d<\/jats:italic>-simplex. We prove that if

$|\\cG| \\geq (1 - o(1))\\binom{n-1 }{k-1}$<\/jats:alt-text><\/jats:inline-graphic>, then there is a vertex x<\/jats:italic> of

<\/jats:private-char> such that the number of sets in

<\/jats:private-char> omitting x<\/jats:italic> is o<\/jats:italic>(n<\/jats:italic>k<\/jats:italic>\u22121<\/jats:sup>) (here o<\/jats:italic>(1)\u2192 0 and n<\/jats:italic> \u2192 \u221e). A similar result when n<\/jats:italic>\/k<\/jats:italic> is bounded from above was recently proved in [10].<\/jats:p>Our main result is actually stronger, and implies that if

$|\\cG| > (1 + \\epsilon)\\binom{n-1 }{ k-1}$<\/jats:alt-text><\/jats:inline-graphic> for any \u03f5 < 0 and n<\/jats:italic> sufficiently large, then

<\/jats:private-char> contains d<\/jats:italic> + 2 sets A<\/jats:italic>, A<\/jats:italic>1<\/jats:sub>, .\u00a0.\u00a0. ,A<\/jats:italic>d<\/jats:italic>+1<\/jats:sub> such that the A<\/jats:italic>i<\/jats:italic><\/jats:sub>s<\/jats:italic> form a d<\/jats:italic>-simplex, and A<\/jats:italic> contains an element of \u2229j<\/jats:italic>\u2260i<\/jats:italic><\/jats:sub>A<\/jats:italic>j<\/jats:italic><\/jats:sub> for each i<\/jats:italic>. This generalizes, in asymptotic form, a recent result of Vestra\u00ebte and the first author [18], who proved it for d<\/jats:italic> = 1, \u03f5 = 0 and n<\/jats:italic> \u2265 2k<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0963548309009705","type":"journal-article","created":{"date-parts":[[2009,2,19]],"date-time":"2009-02-19T06:13:00Z","timestamp":1235023980000},"page":"441-454","source":"Crossref","is-referenced-by-count":7,"title":["Simplex Stability"],"prefix":"10.1017","volume":"18","author":[{"given":"DHRUV","family":"MUBAYI","sequence":"first","affiliation":[]},{"given":"RESHMA","family":"RAMADURAI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,5,1]]},"reference":[{"key":"S0963548309009705_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.04.001"},{"key":"S0963548309009705_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/12.1.313"},{"key":"S0963548309009705_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-005-0042-2"},{"key":"S0963548309009705_ref1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-9.2.355"},{"key":"S0963548309009705_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2006.07.001"},{"key":"S0963548309009705_ref19","unstructured":"[19] Mubayi D. and Verstra\u00ebte J. Two-regular subgraphs of hypergraphs. J. Combin. Theory Ser. B, to appear."},{"key":"S0963548309009705_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2004.12.007"},{"key":"S0963548309009705_ref4","first-page":"1317","volume-title":"Handbook of Combinatorics","author":"Frankl","year":"1995"},{"key":"S0963548309009705_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579190"},{"key":"S0963548309009705_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.05.003"},{"key":"S0963548309009705_ref16","doi-asserted-by":"crossref","unstructured":"[16] Mubayi D. and Ramadurai R. Set systems with union and intersection constraints. J. Combin. Theory Ser. B, to appear.","DOI":"10.1016\/j.jctb.2008.10.004"},{"key":"S0963548309009705_ref2","first-page":"2","volume-title":"Proc. 2nd Louisiana Conf. on Comb., Graph Theory and Computing","author":"Erd\u0151s","year":"1971"},{"key":"S0963548309009705_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2006.11.013"},{"key":"S0963548309009705_ref20","first-page":"279","volume-title":"Theory of Graphs","author":"Simonovits","year":"1968"},{"key":"S0963548309009705_ref14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-06-04009-8"},{"key":"S0963548309009705_ref10","doi-asserted-by":"crossref","unstructured":"[10] Keevash P. and Mubayi D. Set systems without a simplex or a cluster. Combinatorica, to appear.","DOI":"10.1007\/s00493-010-2401-x"},{"key":"S0963548309009705_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-005-0034-2"},{"key":"S0963548309009705_ref6","unstructured":"[6] F\u00fcredi Z. and Ozkahya L. An intersection theorem with small unions. Preprint."},{"key":"S0963548309009705_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-005-0036-0"},{"key":"S0963548309009705_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305006784"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548309009705","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T15:36:34Z","timestamp":1554564994000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548309009705\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,5]]}},"alternative-id":["S0963548309009705"],"URL":"https:\/\/doi.org\/10.1017\/s0963548309009705","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5]]}}}