{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:57:23Z","timestamp":1777129043413,"version":"3.51.4"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2013,3,13]],"date-time":"2013-03-13T00:00:00Z","timestamp":1363132800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Several years ago Linial and Meshulam (Combinatorica 26 (2006) 457\u2013487) introduced a model called <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/rsa20495-math-0001.png\" xlink:title=\"urn:x-wiley:10429832:media:rsa20495:rsa20495-math-0001\"\/> of random <jats:italic>n<\/jats:italic>\u2010vertex <jats:italic>d<\/jats:italic>\u2010dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/rsa20495-math-0002.png\" xlink:title=\"urn:x-wiley:10429832:media:rsa20495:rsa20495-math-0002\"\/> at which the <jats:italic>d<\/jats:italic>\u2010dimensional homology of such a random <jats:italic>d<\/jats:italic>\u2010complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question. \u00a9 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 26\u201335, 2015<\/jats:p>","DOI":"10.1002\/rsa.20495","type":"journal-article","created":{"date-parts":[[2013,3,14]],"date-time":"2013-03-14T07:55:17Z","timestamp":1363247717000},"page":"26-35","source":"Crossref","is-referenced-by-count":24,"title":["When does the top homology of a random simplicial complex vanish?"],"prefix":"10.1002","volume":"46","author":[{"given":"Lior","family":"Aronshtam","sequence":"first","affiliation":[{"name":"Department of Computer Science Hebrew University Jerusalem 91904 Israel"}]},{"given":"Nathan","family":"Linial","sequence":"additional","affiliation":[{"name":"Department of Computer Science Hebrew University Jerusalem 91904 Israel"}]}],"member":"311","published-online":{"date-parts":[[2013,3,13]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/0471722154"},{"key":"e_1_2_8_3_1","unstructured":"L.Aronshtam N.Linial T.\u0141uczak andR.Meshulam Collapsibility and vanishing of top homology in random simplicial complexes. arXiv:1010.1400."},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2010-00677-7"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-011-9378-0"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90087-3"},{"key":"e_1_2_8_7_1","volume-title":"Algebraic topology","author":"Hatcher A.","year":"2002"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2010-10596-8"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0027-9"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9252-5"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107359949.008"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20238"},{"key":"e_1_2_8_13_1","volume-title":"Elements of algebraic topology","author":"Munkres J. 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