{"paper":{"title":"Kostka multiplicity one for multipartitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"C. Ryan Vinroot, James Janopaul-Naylor","submitted_at":"2015-06-23T14:21:28Z","abstract_excerpt":"If $[\\lambda(j)]$ is a multipartition of the positive integer $n$ (a sequence of partitions with total size $n$), and $\\mu$ is a partition of $n$, we study the number $K_{[\\lambda(j)]\\mu}$ of sequences of semistandard Young tableaux of shape $[\\lambda(j)]$ and total weight $\\mu$. We show that the numbers $K_{[\\lambda(j)] \\mu}$ occur naturally as the multiplicities in certain permutation representations of wreath products. The main result is a set of conditions on $[\\lambda(j)]$ and $\\mu$ which are equivalent to $K_{[\\lambda(j)] \\mu} = 1$, generalizing a theorem of Berenshte\\u{\\i}n and Zelevins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07022","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"}