{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:31:08Z","timestamp":1772368268488,"version":"3.50.1"},"reference-count":20,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2019,1,15]],"date-time":"2019-01-15T00:00:00Z","timestamp":1547510400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["339096 (Nati Linial)"],"award-info":[{"award-number":["339096 (Nati Linial)"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005155","name":"Azrieli Foundation","doi-asserted-by":"publisher","award":["Azrieli Fellowship (Yuval Peled)"],"award-info":[{"award-number":["Azrieli Fellowship (Yuval Peled)"]}],"id":[{"id":"10.13039\/501100005155","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p>Over 30 years ago, Kalai proved a beautiful <jats:italic>d<\/jats:italic>\u2010dimensional analog of Cayley's formula for the number of <jats:italic>n<\/jats:italic>\u2010vertex trees. He enumerated <jats:italic>d<\/jats:italic>\u2010dimensional hypertrees weighted by the squared size of their (<jats:italic>d<\/jats:italic>\u2009\u2212\u20091)\u2010dimensional homology group. This, however, does not answer the more basic problem of unweighted enumeration of <jats:italic>d<\/jats:italic>\u2010hypertrees, which is our concern here. Our main result, Theorem 1.4, significantly improves the lower bound for the number of <jats:italic>d<\/jats:italic>\u2010hypertrees. In addition, we study a random 1\u2010out model of <jats:italic>d<\/jats:italic>\u2010complexes where every (<jats:italic>d<\/jats:italic>\u2009\u2212\u20091)\u2010dimensional face selects a random <jats:italic>d<\/jats:italic>\u2010face containing it, and show that it has a negligible <jats:italic>d<\/jats:italic>\u2010dimensional homology.<\/jats:p>","DOI":"10.1002\/rsa.20841","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T04:50:30Z","timestamp":1547614230000},"page":"677-695","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Enumeration and randomized constructions of hypertrees"],"prefix":"10.1002","volume":"55","author":[{"given":"Nati","family":"Linial","sequence":"first","affiliation":[{"name":"Department of Computer Science Hebrew University Jerusalem Israel"}]},{"given":"Yuval","family":"Peled","sequence":"additional","affiliation":[{"name":"Department of Computer Science Hebrew University Jerusalem Israel"}]}],"member":"311","published-online":{"date-parts":[[2019,1,15]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6464"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-13984-5_1"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01285814"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-012-9483-8"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392300"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20272"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04898-3"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/129712.129716"},{"issue":"57","key":"e_1_2_7_10_1","first-page":"2","article-title":"On the number of perfect matchings and Hamilton cycles in \u03f5\u2010regular non\u2010bipartite graphs","volume":"7","author":"Frieze A.","year":"2000","journal-title":"Electron. J. Combin."},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90077-8"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700016517"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579140"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02804017"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9252-5"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2016.184.3.3"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793525309000072"},{"issue":"1","key":"e_1_2_7_18_1","first-page":"148","article-title":"On the method of bounded differences","volume":"141","author":"McDiarmid C.","year":"1989","journal-title":"Surv. Combin."},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90023-1"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(89)90067-9"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/237814.237880"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.20841","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.20841","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T20:21:50Z","timestamp":1693686110000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.20841"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,15]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["10.1002\/rsa.20841"],"URL":"https:\/\/doi.org\/10.1002\/rsa.20841","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,15]]},"assertion":[{"value":"2018-01-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-17","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-01-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}