{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:32:37Z","timestamp":1774369957416,"version":"3.50.1"},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2013,3,5]],"date-time":"2013-03-05T00:00:00Z","timestamp":1362441600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"ISF"},{"name":"BSF"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Richard Wilson conjectured in 1974 the following asymptotic formula for the number of <jats:italic>n<\/jats:italic> \u2010vertex Steiner triple systems:<\/jats:p><jats:p>\n<jats:styled-content>\\documentclass{article}\\usepackage{mathrsfs, amsmath, amssymb}\\pagestyle{empty}\\begin{document}\\begin{align*} STS(n) = \\left( (1+o(1))\\frac{n}{e^2} \\right)^{\\frac{n^2}{6}}\\end{align*}\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\"\/><\/jats:styled-content>. Our main result is that\n<jats:disp-formula>\n\n<\/jats:disp-formula><\/jats:p><jats:p>The proof is based on the entropy method.<\/jats:p><jats:p>As a prelude to this proof we consider the number <jats:italic>F<\/jats:italic>(<jats:italic>n<\/jats:italic>) of 1 \u2010factorizations of the complete graph on <jats:italic>n<\/jats:italic> vertices. Using the Kahn\u2010Lov\u00e1sz theorem it can be shown that\n<jats:disp-formula>\n\n<\/jats:disp-formula>\nWe show how to derive this bound using the entropy method. Both bounds are conjectured to be sharp. \u00a9 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 399\u2013406, 2013<\/jats:p>","DOI":"10.1002\/rsa.20487","type":"journal-article","created":{"date-parts":[[2013,3,5]],"date-time":"2013-03-05T14:33:36Z","timestamp":1362494016000},"page":"399-406","source":"Crossref","is-referenced-by-count":24,"title":["An upper bound on the number of Steiner triple systems"],"prefix":"10.1002","volume":"43","author":[{"given":"Nathan","family":"Linial","sequence":"first","affiliation":[]},{"given":"Zur","family":"Luria","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2013,3,5]]},"reference":[{"key":"e_1_2_5_2_2","doi-asserted-by":"crossref","DOI":"10.37236\/888","article-title":"The maximum number of perfect matchings in graphs with a given degree sequence","volume":"15","author":"Alon N.","year":"2008","journal-title":"Electron J Combin"},{"key":"e_1_2_5_3_2","article-title":"An entropy proof of the Kahn\u2010Lov\u00e1sz theorem","author":"Cutler J.","journal-title":"Electron J Combin"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.07.005"},{"key":"e_1_2_5_5_2","first-page":"144","volume-title":"In London Math. SOC. Lecture Note Ser. 23","author":"Cameron P. J.","year":"1976"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471200611"},{"key":"e_1_2_5_7_2","doi-asserted-by":"crossref","DOI":"10.37236\/497","article-title":"An entropy proof of the Kahn\u2010Lov\u00e1sz theorem","author":"Cutler J.","year":"2011","journal-title":"Electron J Combin"},{"key":"e_1_2_5_8_2","unstructured":"N.Linial Z.Luria An upper bound on the number of higher dimensional permutations submitted for publication and. available at:http:\/\/arxiv.org\/abs\/1106.0649(2011)."},{"key":"e_1_2_5_9_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.2727"},{"key":"e_1_2_5_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511987045"},{"key":"e_1_2_5_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215371"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.20487","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.20487","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.20487","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T20:48:06Z","timestamp":1698526086000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.20487"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,5]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1002\/rsa.20487"],"URL":"https:\/\/doi.org\/10.1002\/rsa.20487","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3,5]]}}}