{"paper":{"title":"Integer concave cocirculations and honeycombs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander V. Karzanov","submitted_at":"2004-01-23T14:55:26Z","abstract_excerpt":"A convex triangular grid is represented by a planar digraph $G$ embedded in the plane so that (a) each bounded face is surrounded by three edges and forms an equilateral triangle, and (b) the union $\\Rscr$ of bounded faces is a convex polygon. A real-valued function $h$ on the edges of $G$ is called a concave cocirculation if $h(e)=g(v)-g(u)$ for each edge $e=(u,v)$, where $g$ is a concave function on $\\Rscr$ which is affinely linear within each bounded face of $G$. Knutson and Tao [J. Amer. Math. Soc. 12 (4) (1999) 1055--1090] proved an integrality theorem for so-called honeycombs, which is e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401313","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"}