{"paper":{"title":"A Counting Lov\\'asz Local Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Can Zhou, Chunyang Wang, Hongyang Liu, Yitong Yin, Yiyao Zhang","submitted_at":"2026-08-09T10:05:13Z","abstract_excerpt":"We establish a counting analogue of the Lov\\'asz Local Lemma: we give polynomial-time algorithms for approximately counting satisfying assignments of general constraint satisfaction problems (CSPs) in the local lemma regime $$ 4 \\mathrm{e}\\cdot p\\cdot (D+1)^2\\leq 1, $$ where $p$ is the maximum constraint violation probability and $D$ is the maximum dependency degree.\n  This condition is tight up to constant factors, matching known lower bounds $pD^2\\gtrsim 1$ for approximate counting in natural subclasses of CSPs. The core of our approach is a novel $2$-tree expansion for constraint marginal p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08616","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08616/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}