{"paper":{"title":"Asymptotics of principal evaluations of Schubert polynomials for layered permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro H. Morales, Greta Panova, Igor Pak","submitted_at":"2018-05-11T11:49:19Z","abstract_excerpt":"Denote by $u(n)$ the largest principal specialization of the Schubert polynomial: $\nu(n) := \\max_{w \\in S_n} \\mathfrak{S}_w(1,\\ldots,1) $ Stanley conjectured in [arXiv:1704.00851] that there is a limit $\\lim_{n\\to \\infty} \\, \\frac{1}{n^2} \\log u(n), $ and asked for a limiting description of permutations achieving the maximum $u(n)$. Merzon and Smirnov conjectured in [arXiv:1410.6857] that this maximum is achieved on layered permutations. We resolve both Stanley's problems restricted to layered permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04341","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"}