{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:36Z","timestamp":1759335636869,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Asymptotic calculations are applied to study  the degrees of certain sequences of characters of symmetric groups.  Starting with a given partition $\\mu$, we deduce several skew diagrams  which are related to $\\mu$. To each such skew diagram there corresponds  the product of its hook numbers. By asymptotic methods we obtain some  unexpected arithmetic properties between these products.  The authors do  not know \"finite\", nonasymptotic proofs of these results. The problem  appeared in the study of the hook formula for various kinds of Young  diagrams. The proofs are based on properties of shifted Schur functions,  due to Okounkov and Olshanski. The theory of these functions arose from  the asymptotic theory of Vershik and Kerov of the representations of the  symmetric groups.<\/jats:p>","DOI":"10.37236\/1307","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:53:29Z","timestamp":1578707609000},"source":"Crossref","is-referenced-by-count":7,"title":["Asymptotics of Young Diagrams and Hook Numbers"],"prefix":"10.37236","volume":"4","author":[{"given":"Amitai","family":"Regev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anatoly","family":"Vershik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1997,9,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r22\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:11:35Z","timestamp":1579327895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v4i1r22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,9,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1997,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1307","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1997,9,21]]},"article-number":"R22"}}