{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:R6LD2VWXWJG4DAT36JJJ2ZMZLO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed989bb1b2365d0a0db9f6653cfd6a55c1a6ccdec887e9d634ea1ecb3b3109ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-21T20:59:51Z","title_canon_sha256":"7706677737db9a9262740be0a97ed3ea29f2f926671212d9e5393aa8ae53c545"},"schema_version":"1.0","source":{"id":"1009.4214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4214","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4214v2","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4214","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"R6LD2VWXWJG4","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R6LD2VWXWJG4DAT3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R6LD2VWX","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:de87cfd608a7996517b34c822b7f5be5c2faf543d6e7a8c70b415e8ad5063447","target":"graph","created_at":"2026-05-18T04:40:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which possibly contains repetitions, taking some or all of the elements at a time, in any imposed order. The algorithm uses an auxiliary array that maintains the number of occurrences of each unique element in the input list. We provide a proof of correctness of the algorithm. We then show how one can efficiently generate other combinatorial structures like combinat","authors_text":"Pramod Ganapathi, Rama B","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-21T20:59:51Z","title":"A Versatile Algorithm to Generate Various Combinatorial Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4214","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a371de79e366f870fd67f5bc125785aad321009a4a756f6262975252946eb943","target":"record","created_at":"2026-05-18T04:40:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ed989bb1b2365d0a0db9f6653cfd6a55c1a6ccdec887e9d634ea1ecb3b3109ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-21T20:59:51Z","title_canon_sha256":"7706677737db9a9262740be0a97ed3ea29f2f926671212d9e5393aa8ae53c545"},"schema_version":"1.0","source":{"id":"1009.4214","kind":"arxiv","version":2}},"canonical_sha256":"8f963d56d7b24dc1827bf2529d65995baeb76bbc737de38ab37e34c7e6989c88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f963d56d7b24dc1827bf2529d65995baeb76bbc737de38ab37e34c7e6989c88","first_computed_at":"2026-05-18T04:40:08.044003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:08.044003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/zjXC3BKRKKV3jWmyXochAAxa9bKxd0oKivmYS4HjlOEAGTx8gMM1dwpIUU5UaWTZFSi13yzTALRTf+S3pACCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:08.044681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a371de79e366f870fd67f5bc125785aad321009a4a756f6262975252946eb943","sha256:de87cfd608a7996517b34c822b7f5be5c2faf543d6e7a8c70b415e8ad5063447"],"state_sha256":"eab3151a81e03563c20be1968ef78155259c1369795c4ab86a18d7f560256957"}