{"paper":{"title":"Flow polytopes with Catalan volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jang Soo Kim, Karola M\\'esz\\'aros, Sylvie Corteel","submitted_at":"2016-12-01T01:15:00Z","abstract_excerpt":"The Chan-Robbins-Yuen polytope can be thought of as the flow polytope of the complete graph with netflow vector $(1, 0, \\ldots, 0, -1)$. The normalized volume of the Chan-Robbins-Yuen polytope equals the product of consecutive Catalan numbers, yet there is no combinatorial proof of this fact. We consider a natural generalization of this polytope, namely, the flow polytope of the complete graph with netflow vector $(1,1, 0, \\ldots, 0, -2)$. We show that the volume of this polytope is a certain power of $2$ times the product of consecutive Catalan numbers. Our proof uses constant term identities"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00102","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"}