{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:36:36Z","timestamp":1787506596098,"version":"build-2736575974"},"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>The Kronecker product of two Schur functions $s_{\\lambda}$ and $s_{\\mu}$, denoted $s_{\\lambda}\\ast s_{\\mu}$, is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of $n$, $\\lambda$ and $\\mu$, respectively. The coefficient, $g_{\\lambda,\\mu,\\nu}$, of $s_{\\nu}$ in $s_{\\lambda}\\ast s_{\\mu}$ is equal to the multiplicity of the irreducible representation indexed by $\\nu$ in the tensor product.  In this paper we give an algorithm for expanding the Kronecker product $s_{(n-p,p)}\\ast s_{\\lambda}$ if $\\lambda_1-\\lambda_2\\geq 2p$.  As a consequence of this algorithm we obtain a formula for $g_{(n-p,p), \\lambda ,\\nu}$ in terms of the Littlewood-Richardson coefficients which does not involve cancellations. Another consequence of our algorithm is that if $\\lambda_1-\\lambda_2\\geq 2p$ then every Kronecker coefficient in $s_{(n-p,p)}\\ast s_{\\lambda}$ is independent of $n$, in other words, $g_{(n-p,p),\\lambda,\\nu}$ is stable for all $\\nu$.<\/jats:p>","DOI":"10.37236\/1925","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:11:38Z","timestamp":1578701498000},"source":"Crossref","is-referenced-by-count":10,"title":["On the Kronecker Product  $s_{(n-p,p)}\\ast s_{\\lambda}$"],"prefix":"10.37236","volume":"12","author":[{"given":"C. M.","family":"Ballantine","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. C.","family":"Orellana","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2005,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:49:26Z","timestamp":1579304966000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1925","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6,14]]},"article-number":"R28"}}