{"paper":{"title":"Counting hypergraph colorings in the local lemma regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Chao Liao, Chihao Zhang, Heng Guo, Pinyan Lu","submitted_at":"2017-11-09T14:49:59Z","abstract_excerpt":"We give a fully polynomial-time approximation scheme (FPTAS) to count the number of $q$-colorings for $k$-uniform hypergraphs with maximum degree $\\Delta$ if $k\\ge 28$ and $q >357\\Delta^{\\frac{14}{k-14}}$ . We also obtain a polynomial-time almost uniform sampler if $q>931\\Delta^{\\frac{16}{k-16/3}}$. These are the first approximate counting and sampling algorithms in the regime $q\\ll\\Delta$ (for large $\\Delta$ and $k$) without any additional assumptions. Our method is based on the recent work of Moitra (STOC, 2017). One important contribution of ours is to remove the dependency of $k$ and $\\Del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03396","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"}