{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:R6LD2VWXWJG4DAT36JJJ2ZMZLO","short_pith_number":"pith:R6LD2VWX","schema_version":"1.0","canonical_sha256":"8f963d56d7b24dc1827bf2529d65995baeb76bbc737de38ab37e34c7e6989c88","source":{"kind":"arxiv","id":"1009.4214","version":2},"attestation_state":"computed","paper":{"title":"A Versatile Algorithm to Generate Various Combinatorial Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pramod Ganapathi, Rama B","submitted_at":"2010-09-21T20:59:51Z","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"},"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":"1009.4214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-21T20:59:51Z","cross_cats_sorted":[],"title_canon_sha256":"7706677737db9a9262740be0a97ed3ea29f2f926671212d9e5393aa8ae53c545","abstract_canon_sha256":"ed989bb1b2365d0a0db9f6653cfd6a55c1a6ccdec887e9d634ea1ecb3b3109ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:08.044681Z","signature_b64":"/zjXC3BKRKKV3jWmyXochAAxa9bKxd0oKivmYS4HjlOEAGTx8gMM1dwpIUU5UaWTZFSi13yzTALRTf+S3pACCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f963d56d7b24dc1827bf2529d65995baeb76bbc737de38ab37e34c7e6989c88","last_reissued_at":"2026-05-18T04:40:08.044003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:08.044003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Versatile Algorithm to Generate Various Combinatorial Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pramod Ganapathi, Rama B","submitted_at":"2010-09-21T20:59:51Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4214","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":"1009.4214","created_at":"2026-05-18T04:40:08.044109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4214v2","created_at":"2026-05-18T04:40:08.044109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4214","created_at":"2026-05-18T04:40:08.044109+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6LD2VWXWJG4","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6LD2VWXWJG4DAT3","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6LD2VWX","created_at":"2026-05-18T12:26:13.927090+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/R6LD2VWXWJG4DAT36JJJ2ZMZLO","json":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO.json","graph_json":"https://pith.science/api/pith-number/R6LD2VWXWJG4DAT36JJJ2ZMZLO/graph.json","events_json":"https://pith.science/api/pith-number/R6LD2VWXWJG4DAT36JJJ2ZMZLO/events.json","paper":"https://pith.science/paper/R6LD2VWX"},"agent_actions":{"view_html":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO","download_json":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO.json","view_paper":"https://pith.science/paper/R6LD2VWX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4214&json=true","fetch_graph":"https://pith.science/api/pith-number/R6LD2VWXWJG4DAT36JJJ2ZMZLO/graph.json","fetch_events":"https://pith.science/api/pith-number/R6LD2VWXWJG4DAT36JJJ2ZMZLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO/action/storage_attestation","attest_author":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO/action/author_attestation","sign_citation":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO/action/citation_signature","submit_replication":"https://pith.science/pith/R6LD2VWXWJG4DAT36JJJ2ZMZLO/action/replication_record"}},"created_at":"2026-05-18T04:40:08.044109+00:00","updated_at":"2026-05-18T04:40:08.044109+00:00"}