{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VIEFA4S7KJS5PI7ZUFATMXLLAW","short_pith_number":"pith:VIEFA4S7","schema_version":"1.0","canonical_sha256":"aa0850725f5265d7a3f9a141365d6b059519d5572157145fcd42c14d27b2286f","source":{"kind":"arxiv","id":"1102.0041","version":2},"attestation_state":"computed","paper":{"title":"Consecutive Ones Property and PQ-Trees for Multisets: Hardness of Counting Their Orderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Giovanni Battaglia, Noemi Scutell\\`a, Roberto Grossi","submitted_at":"2011-01-31T23:59:40Z","abstract_excerpt":"A binary matrix satisfies the consecutive ones property (COP) if its columns can be permuted such that the ones in each row of the resulting matrix are consecutive. Equivalently, a family of sets F = {Q_1,..,Q_m}, where Q_i is subset of R for some universe R, satisfies the COP if the symbols in R can be permuted such that the elements of each set Q_i occur consecutively, as a contiguous segment of the permutation of R's symbols. We consider the COP version on multisets and prove that counting its solutions is difficult (#P-complete). We prove completeness results also for counting the frontier"},"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":"1102.0041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-31T23:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"32b917dde4c995b9a129a34708d6a501570c83f3a83cb4f0487764be052c002a","abstract_canon_sha256":"01962fe2acbf71da14564c282a20fd07d1f3c29cfd84739bd378afd62e5d9adb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:41.543797Z","signature_b64":"/0S6Yd2jV2wrOcBHmqSRvkKY9Fa6K0wYhSH0HxOWZ6x3mG4OPOuMrQr8ZT+ywO7rpu4d4/Bl6vNRDJtmQILVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa0850725f5265d7a3f9a141365d6b059519d5572157145fcd42c14d27b2286f","last_reissued_at":"2026-05-18T02:22:41.543272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:41.543272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consecutive Ones Property and PQ-Trees for Multisets: Hardness of Counting Their Orderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Giovanni Battaglia, Noemi Scutell\\`a, Roberto Grossi","submitted_at":"2011-01-31T23:59:40Z","abstract_excerpt":"A binary matrix satisfies the consecutive ones property (COP) if its columns can be permuted such that the ones in each row of the resulting matrix are consecutive. Equivalently, a family of sets F = {Q_1,..,Q_m}, where Q_i is subset of R for some universe R, satisfies the COP if the symbols in R can be permuted such that the elements of each set Q_i occur consecutively, as a contiguous segment of the permutation of R's symbols. We consider the COP version on multisets and prove that counting its solutions is difficult (#P-complete). We prove completeness results also for counting the frontier"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0041","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.0041","created_at":"2026-05-18T02:22:41.543348+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0041v2","created_at":"2026-05-18T02:22:41.543348+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0041","created_at":"2026-05-18T02:22:41.543348+00:00"},{"alias_kind":"pith_short_12","alias_value":"VIEFA4S7KJS5","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VIEFA4S7KJS5PI7Z","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VIEFA4S7","created_at":"2026-05-18T12:26:44.992195+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/VIEFA4S7KJS5PI7ZUFATMXLLAW","json":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW.json","graph_json":"https://pith.science/api/pith-number/VIEFA4S7KJS5PI7ZUFATMXLLAW/graph.json","events_json":"https://pith.science/api/pith-number/VIEFA4S7KJS5PI7ZUFATMXLLAW/events.json","paper":"https://pith.science/paper/VIEFA4S7"},"agent_actions":{"view_html":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW","download_json":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW.json","view_paper":"https://pith.science/paper/VIEFA4S7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0041&json=true","fetch_graph":"https://pith.science/api/pith-number/VIEFA4S7KJS5PI7ZUFATMXLLAW/graph.json","fetch_events":"https://pith.science/api/pith-number/VIEFA4S7KJS5PI7ZUFATMXLLAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW/action/storage_attestation","attest_author":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW/action/author_attestation","sign_citation":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW/action/citation_signature","submit_replication":"https://pith.science/pith/VIEFA4S7KJS5PI7ZUFATMXLLAW/action/replication_record"}},"created_at":"2026-05-18T02:22:41.543348+00:00","updated_at":"2026-05-18T02:22:41.543348+00:00"}