{"paper":{"title":"On compositions associated to seasweed subalgebras of sl(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew W. Mayers, Aria Dougherty, jr, Matthew Hyatt, Nick W. Mayers, Vincent E. Coll","submitted_at":"2018-08-02T20:23:10Z","abstract_excerpt":"A standard seaweed subalgebra of $A_{n-1}=\\mathfrak{sl}(n)$ may be parametrized by a pair of compositions of the positive integer $n$. For all $n$ and certain $k(n)$, we provide closed-form formulas and the generating functions for $C(n,k)$ -- the number of parametrizing pairs which yield a seaweed subalgebra of $\\mathfrak{sl}(n)$ of index $k$. Our analysis sets the framework for addressing similar questions in the other classical families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01008","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"}