{"paper":{"title":"Proof of Lassalle's Positivity Conjecture on Schur Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anne X. Y. Ren, Arthur L. B. Yang, William Y. C. Chen","submitted_at":"2012-09-01T10:11:38Z","abstract_excerpt":"In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let $(t)_n$ denote the rising factorial, and let $\\Lambda_{\\mathbb{R}}$ denote the algebra of symmetric functions with real coefficients. If $\\varphi$ is the homomorphism from $\\Lambda_{\\mathbb{R}}$ to $\\mathbb{R}$ defined by $\\varphi(h_n)={1}/{((t)_nn!)}$ for some $t>0$, then for any Schur function $s_{\\lambda}$, the value $\\varphi(s_{\\lambda})$ is positive. In this paper, we provide an affirmative answer to Lassalle's conjecture by using the Laguerre-P\\'o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0078","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"}