{"paper":{"title":"Root polytope and partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Rocco Chirivi'","submitted_at":"2012-10-31T16:30:28Z","abstract_excerpt":"Given a crystallographic reduced root system and an element v of the lattice generated by the roots we study the minimum number |v|, called the length of v, of roots needed to express v as sum of roots. This number is related to the linear functionals presenting the convex hull of the roots; the map v --> |v| turns out to be piecewise quasi-linear with quasi-linearity domains the cones over the facets of this convex hull. In order to show this relation we investigate the integral closure of the monoid generated by the roots in a facet. We study also the positive lenght, i.e. the minimum number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8379","kind":"arxiv","version":3},"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"}