{"paper":{"title":"Combinatorics of the Lipschitz polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"F. Petrov, J. Gordon","submitted_at":"2016-08-24T14:50:23Z","abstract_excerpt":"Let $\\rho$ be a metric on the set $X=\\{1,2,\\dots,n+1\\}$. Consider the $n$-dimensional polytope of functions $f:X\\rightarrow \\mathbb{R}$, which satisfy the conditions $f(n+1)=0$, $|f(x)-f(y)|\\leq \\rho(x,y)$. The question on classifying metrics depending on the combinatorics of this polytope have been recently posed by A. M. Vershik \\cite{V}. We prove that for any \"generic\" metric the number of $(n-m)$-dimensional faces, $0\\leq m\\leq n$, equals $\\binom{n+m}{m,m,n-m}=(n+m)!/m!m!(n-m)!$. This fact is intimately related to regular triangulations of the root polytope (the convex hull of the roots of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06848","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"}