{"paper":{"title":"The face vector of a half-open hypersimplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hidefumi Ohsugi, Nan Li, Takayuki Hibi","submitted_at":"2013-09-20T02:05:03Z","abstract_excerpt":"The half-open hypersimplex $\\Delta'_{n,k}$ consists of those $x = (x_{1}, \\ldots, x_{n}) \\in[0,1]^n$ with $k-1<x_1+\\cdots+x_n\\le k$, where $0 < k \\leq n$. The $f$-vector of a half-open hypersimplex and related generating functions are explicitly studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5155","kind":"arxiv","version":2},"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"}