{"paper":{"title":"On the complexity of computing Kronecker coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.RT"],"primary_cat":"math.CO","authors_text":"Greta Panova, Igor Pak","submitted_at":"2014-04-02T19:01:31Z","abstract_excerpt":"We study the complexity of computing Kronecker coefficients $g(\\lambda,\\mu,\\nu)$. We give explicit bounds in terms of the number of parts $\\ell$ in the partitions, their largest part size $N$ and the smallest second part $M$ of the three partitions. When $M = O(1)$, i.e. one of the partitions is hook-like, the bounds are linear in $\\log N$, but depend exponentially on $\\ell$. Moreover, similar bounds hold even when $M=e^{O(\\ell)}$. By a separate argument, we show that the positivity of Kronecker coefficients can be decided in $O(\\log N)$ time for a bounded number $\\ell$ of parts and without re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0653","kind":"arxiv","version":3},"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"}