{"paper":{"title":"Recursive algorithm and log-concavity of representations on the cohomology of $\\overline{\\mathcal M}_{0,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Donggun Lee, Jinwon Choi, Young-Hoon Kiem","submitted_at":"2024-08-20T10:56:04Z","abstract_excerpt":"We provide a programmable recursive algorithm for the $\\mathbb{S}_n$-representations on the cohomology of the moduli spaces $\\overline{\\mathcal M}_{0,n}$ of $n$-pointed stable curves of genus 0. As an application, we find explicit inductive and asymptotic formulas for the invariant part $H^*(\\overline{\\mathcal M}_{0,n}/\\mathbb{S}_n)$ and prove that its Poincar\\'e polynomial is asymptotically log-concave. Based on numerical computations with our algorithm, we further conjecture that the sequence $\\{H^{2k}(\\overline{\\mathcal M}_{0,n})\\}$ of $\\mathbb{S}_n$-modules is equivariantly log-concave."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10728","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.10728/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}