{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:06:08Z","timestamp":1772445968652,"version":"3.50.1"},"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>F. Murnaghan observed a long time ago that the computation of the decompositon of the Kronecker product $\\chi^{(n-a, \\lambda_2, \\dots )}\\otimes \\chi^{(n-b, \\mu_2, \\dots)}$ of two irreducible characters of the symmetric group into irreducibles depends only on $\\overline\\lambda=(\\lambda_2,\\dots )$ and $\\overline\\mu =(\\mu_2,\\dots )$, but not on $n$. In this note we prove a similar result: given three partitions $\\lambda$, $\\mu$, $\\nu$ of $n$ we obtain a lower bound on $n$, depending on $\\overline\\lambda$, $\\overline\\mu$, $\\overline\\nu$, for the stability of the multiplicity $c(\\lambda,\\mu,\\nu)$ of $\\chi^\\nu$ in $\\chi^\\lambda \\otimes \\chi^\\mu$. Our proof is purely combinatorial. It uses a description of the $c(\\lambda,\\mu,\\nu)$'s in terms of signed special rim hook tabloids and   Littlewood-Richardson multitableaux.<\/jats:p>","DOI":"10.37236\/1471","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:12Z","timestamp":1578708012000},"source":"Crossref","is-referenced-by-count":16,"title":["Stability of Kronecker Products of Irreducible Characters of the Symmetric Group"],"prefix":"10.37236","volume":"6","author":[{"given":"Ernesto","family":"Vallejo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,9,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:32:24Z","timestamp":1579325544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,9,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1471","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,9,6]]},"article-number":"R39"}}