{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DMAQR5WXZ5DBNS4LHII4JC5PTQ","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":"edb639693a9cf64622dff22062179071801ef2450eb0204f8699de4856172aa4","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-29T13:42:37Z","title_canon_sha256":"7af7b4c0050c999c0134cf16bc55c9bb3146566224836a285946d3437c3f62c1"},"schema_version":"1.0","source":{"id":"1607.08806","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08806","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08806v6","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08806","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"DMAQR5WXZ5DB","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DMAQR5WXZ5DBNS4L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DMAQR5WX","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:7380f8b437538132d44f3614710c803e1daed548051f940bc0a6dd4467f38bd1","target":"graph","created_at":"2026-05-18T00:23:17Z","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":"We consider the algorithmic problem of generating each subset of $[n]:=\\{1,2,\\ldots,n\\}$ whose size is in some interval $[k,l]$, $0\\leq k\\leq l\\leq n$, exactly once (cyclically) by repeatedly adding or removing a single element, or by exchanging a single element. For $k=0$ and $l=n$ this is the classical problem of generating all $2^n$ subsets of $[n]$ by element additions/removals, and for $k=l$ this is the classical problem of generating all $\\binom{n}{k}$ subsets of $[n]$ by element exchanges. We prove the existence of such cyclic minimum-change enumerations for a large range of values $n$,","authors_text":"Petr Gregor, Torsten M\\\"utze","cross_cats":["cs.DM","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-29T13:42:37Z","title":"Trimming and gluing Gray codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08806","kind":"arxiv","version":6},"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":"sha256:03fce9aeeb462f0e055ebc2511e46fef4a3e0ceea68650aafc26824d29c57cc4","target":"record","created_at":"2026-05-18T00:23:17Z","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":"edb639693a9cf64622dff22062179071801ef2450eb0204f8699de4856172aa4","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-29T13:42:37Z","title_canon_sha256":"7af7b4c0050c999c0134cf16bc55c9bb3146566224836a285946d3437c3f62c1"},"schema_version":"1.0","source":{"id":"1607.08806","kind":"arxiv","version":6}},"canonical_sha256":"1b0108f6d7cf4616cb8b3a11c48baf9c050683b0b77940f3331177c1135d0c6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b0108f6d7cf4616cb8b3a11c48baf9c050683b0b77940f3331177c1135d0c6f","first_computed_at":"2026-05-18T00:23:17.237348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:17.237348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lN/7NPeDIOm+ELSh3H8G71AXjfin/o3nBf7RSv390BMZ6j9wdOV8g2rvzhO/Vy0wmPVszjlcvgRc/eDdIn2mBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:17.237885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08806","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03fce9aeeb462f0e055ebc2511e46fef4a3e0ceea68650aafc26824d29c57cc4","sha256:7380f8b437538132d44f3614710c803e1daed548051f940bc0a6dd4467f38bd1"],"state_sha256":"f4a7a6007a023af7938c51645f4a86fd4df1bb6ad5a6fd000f604803ec98f87e"}