{"paper":{"title":"Gelfand-Tsetlin polytopes and the integer decomposition property","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Per Alexandersson","submitted_at":"2014-05-19T13:41:36Z","abstract_excerpt":"Let $P$ be the Gelfand--Tsetlin polytope defined by the skew shape $\\lambda/\\mu$ and weight $w$. In the case corresponding to a standard Young tableau, we completely characterize for which shapes $\\lambda/\\mu$ the polytope $P$ is integral. Furthermore, we show that $P$ is a compressed polytope whenever it is integral and corresponds to a standard Young tableau. We conjecture that a similar property hold for arbitrary $w$, namely that $P$ has the integer decomposition property whenever it is integral.\n  Finally, a natural partial ordering on GT-polytopes is introduced that provides information "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4718","kind":"arxiv","version":4},"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"}