{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T02:10:14Z","timestamp":1692929414471},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2017,8,14]],"date-time":"2017-08-14T00:00:00Z","timestamp":1502668800000},"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":[[2018,3]]},"abstract":"<jats:p>A cutset is a non-empty finite subset of \u2124<jats:italic><jats:sup>d<\/jats:sup><\/jats:italic>which is both connected and co-connected. A cutset is odd if its vertex boundary lies in the odd bipartition class of \u2124<jats:italic><jats:sup>d<\/jats:sup><\/jats:italic>. Peled [18] suggested that the number of odd cutsets which contain the origin and have<jats:italic>n<\/jats:italic>boundary edges may be of order<jats:italic>e<\/jats:italic><jats:sup>\u0398(<jats:italic>n\/d<\/jats:italic>)<\/jats:sup>as<jats:italic>d<\/jats:italic>\u2192 \u221e, much smaller than the number of general cutsets, which was shown by Lebowitz and Mazel [15] to be of order<jats:italic>d<\/jats:italic><jats:sup>\u0398(<jats:italic>n\/d<\/jats:italic>)<\/jats:sup>. In this paper, we verify this by showing that the number of such odd cutsets is (2+<jats:italic>o<\/jats:italic>(1))<jats:sup><jats:italic>n<\/jats:italic>\/2<jats:italic>d<\/jats:italic><\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0963548317000438","type":"journal-article","created":{"date-parts":[[2017,8,14]],"date-time":"2017-08-14T08:48:47Z","timestamp":1502700527000},"page":"208-227","source":"Crossref","is-referenced-by-count":0,"title":["The Growth Constant of Odd Cutsets in High Dimensions"],"prefix":"10.1017","volume":"27","author":[{"given":"OHAD NOY","family":"FELDHEIM","sequence":"first","affiliation":[]},{"given":"YINON","family":"SPINKA","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,8,14]]},"reference":[{"key":"S0963548317000438_ref21","first-page":"74","article-title":"The number of antichains in ranked partially ordered sets","volume":"1","author":"Sapozhenko","year":"1989","journal-title":"Diskretnaya Matematika"},{"key":"S0963548317000438_ref20","first-page":"42","article-title":"On the number of connected subsets with given cardinality of the boundary in bipartite graphs (in Russian)","volume":"45","author":"Sapozhenko","year":"1987","journal-title":"Metody Diskretnogo Analiza"},{"key":"S0963548317000438_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(75)90058-8"},{"key":"S0963548317000438_ref10","unstructured":"Galvin D. and Tetali P. 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