{"paper":{"title":"A Combinatorial Interpretation for the coefficients in the Kronecker Product $s_{(n-p,p)}\\ast s_{\\lambda}$ (Multiplicities in the Kronecker Product $s_{(n-p,p)}\\ast s_{\\lambda}$)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristina M. Ballantine, Rosa C. Orellana","submitted_at":"2005-07-26T17:16:56Z","abstract_excerpt":"In this paper we give a combinatorial interpretation for the coefficient of $s_{\\nu}$ in the Kronecker product $s_{(n-p,p)}\\ast s_{\\lambda}$, where $\\lambda=(\\lambda_1, ..., \\lambda_{\\ell(\\lambda)})\\vdash n$, if $\\ell(\\lambda)\\geq 2p-1$ or $\\lambda_1\\geq 2p-1$; that is, if $\\lambda$ is not a partition inside the $2(p-1)\\times 2(p-1)$ square. For $\\lambda$ inside the square our combinatorial interpretation provides an upper bound for the coefficients. In general, we are able to combinatorially compute these coefficients for all $\\lambda$ when $n>(2p-2)^2$. We use this combinatorial interpretati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507544","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}