{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JELR6O5CD5QXUB22WA4OGVBKMZ","short_pith_number":"pith:JELR6O5C","schema_version":"1.0","canonical_sha256":"49171f3ba21f617a075ab038e3542a665f62b77b4e7d5eeed5295f665cd154f5","source":{"kind":"arxiv","id":"1711.03396","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.03396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-09T14:49:59Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"f48412db6e76568c3f65b622e57e34aa30778c4419e51e39a4c54708bcb02911","abstract_canon_sha256":"48bf6e5b6fcdcb3d91e630a73ff11424c6bef4d785b3e45f6baad8962c43b694"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:38.389782Z","signature_b64":"RvP3PjSpYWxs7l1eGrnCj475gia0XsE6SUMOd9QceXauHzUA7u07hN1jdmwgnig5xErNop3voOB3GotYVb86AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49171f3ba21f617a075ab038e3542a665f62b77b4e7d5eeed5295f665cd154f5","last_reissued_at":"2026-05-17T23:44:38.389395Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:38.389395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.03396","created_at":"2026-05-17T23:44:38.389456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.03396v3","created_at":"2026-05-17T23:44:38.389456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03396","created_at":"2026-05-17T23:44:38.389456+00:00"},{"alias_kind":"pith_short_12","alias_value":"JELR6O5CD5QX","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JELR6O5CD5QXUB22","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JELR6O5C","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ","json":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ.json","graph_json":"https://pith.science/api/pith-number/JELR6O5CD5QXUB22WA4OGVBKMZ/graph.json","events_json":"https://pith.science/api/pith-number/JELR6O5CD5QXUB22WA4OGVBKMZ/events.json","paper":"https://pith.science/paper/JELR6O5C"},"agent_actions":{"view_html":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ","download_json":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ.json","view_paper":"https://pith.science/paper/JELR6O5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.03396&json=true","fetch_graph":"https://pith.science/api/pith-number/JELR6O5CD5QXUB22WA4OGVBKMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JELR6O5CD5QXUB22WA4OGVBKMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ/action/storage_attestation","attest_author":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ/action/author_attestation","sign_citation":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ/action/citation_signature","submit_replication":"https://pith.science/pith/JELR6O5CD5QXUB22WA4OGVBKMZ/action/replication_record"}},"created_at":"2026-05-17T23:44:38.389456+00:00","updated_at":"2026-05-17T23:44:38.389456+00:00"}