{"paper":{"title":"On the combinatorics of string polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Eunjeong Lee, Kyeong-Dong Park, Yoosik Kim, Yunhyung Cho","submitted_at":"2019-03-30T01:29:20Z","abstract_excerpt":"For a reduced word ${\\bf i}$ of the longest element in the Weyl group of $\\mathrm{SL}_{n+1}(\\mathbb{C})$, one can associate the string cone $C_{\\bf i}$ which parametrizes the dual canonical bases. In this paper, we classify all ${\\bf i}$'s such that $C_{\\bf i}$ is simplicial. We also prove that for any regular dominant weight $\\lambda$ of $\\mathfrak{sl}_{n+1}(\\mathbb{C})$, the corresponding string polytope $\\Delta_{\\bf i}(\\lambda)$ is unimodularly equivalent to the Gelfand-Cetlin polytope associated to $\\lambda$ if and only if $C_{\\bf i}$ is simplicial. Thus we completely characterize Gelfand-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00130","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"}