{"paper":{"title":"Reconstructing Partitions from their Multisets of $k$-Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Pakawut Jiradilok","submitted_at":"2016-10-17T20:54:20Z","abstract_excerpt":"For non-negative integers $n$ and $k$ with $n \\ge k$, a {\\em $k$-minor} of a partition $\\lambda = [\\lambda_1, \\lambda_2, \\dots]$ of $n$ is a partition $\\mu = [\\mu_1, \\mu_2, \\dots]$ of $n-k$ such that $\\mu_i \\le \\lambda_i$ for all $i$. The multiset $\\widehat{M}_k(\\lambda)$ of $k$-minors of $\\lambda$ is defined as the multiset of $k$-minors $\\mu$ with multiplicity of $\\mu$ equal to the number of standard Young tableaux of skew shape $\\lambda / \\mu$. We show that there exists a function $G(n)$ such that the partitions of $n$ can be reconstructed from their multisets of $k$-minors if and only if $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05354","kind":"arxiv","version":1},"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"}