{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:O2YW3ZC2JBI5AT6LEDDUVC6NEF","short_pith_number":"pith:O2YW3ZC2","schema_version":"1.0","canonical_sha256":"76b16de45a4851d04fcb20c74a8bcd2166c8ef216b8294459403a3322e67ed26","source":{"kind":"arxiv","id":"1404.2359","version":3},"attestation_state":"computed","paper":{"title":"Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"James East, Robert Gray","submitted_at":"2014-04-09T03:57:52Z","abstract_excerpt":"We study the ideals of the partition, Brauer, and Jones monoid, establishing various combinatorial results on generating sets and idempotent generating sets via an analysis of their Graham--Houghton graphs. We show that each proper ideal of the partition monoid P_n is an idempotent generated semigroup, and obtain a formula for the minimal number of elements (and the minimal number of idempotent elements) needed to generate these semigroups. In particular, we show that these two numbers, which are called the rank and idempotent rank (respectively) of the semigroup, are equal to each other, and "},"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":"1404.2359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T03:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"28d78a8c45343231d2408d1733fe521daaf53a7254c903f0d238f199548151b5","abstract_canon_sha256":"215454b9fde9bda3eb405c306f3d7ba0ec4a10087d9e17e33550970ced4c180a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.300306Z","signature_b64":"nicDjdx28vd1AT/m9/wDja2o/CoHWOcYWBnKeAyB5BbYn4mstx6qHG9YtOSPbJIQt8RCiFSsEawgE2WH916SBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76b16de45a4851d04fcb20c74a8bcd2166c8ef216b8294459403a3322e67ed26","last_reissued_at":"2026-05-18T01:09:07.299775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.299775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"James East, Robert Gray","submitted_at":"2014-04-09T03:57:52Z","abstract_excerpt":"We study the ideals of the partition, Brauer, and Jones monoid, establishing various combinatorial results on generating sets and idempotent generating sets via an analysis of their Graham--Houghton graphs. We show that each proper ideal of the partition monoid P_n is an idempotent generated semigroup, and obtain a formula for the minimal number of elements (and the minimal number of idempotent elements) needed to generate these semigroups. In particular, we show that these two numbers, which are called the rank and idempotent rank (respectively) of the semigroup, are equal to each other, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2359","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":"1404.2359","created_at":"2026-05-18T01:09:07.299856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2359v3","created_at":"2026-05-18T01:09:07.299856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2359","created_at":"2026-05-18T01:09:07.299856+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2YW3ZC2JBI5","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2YW3ZC2JBI5AT6L","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2YW3ZC2","created_at":"2026-05-18T12:28:41.024544+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/O2YW3ZC2JBI5AT6LEDDUVC6NEF","json":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF.json","graph_json":"https://pith.science/api/pith-number/O2YW3ZC2JBI5AT6LEDDUVC6NEF/graph.json","events_json":"https://pith.science/api/pith-number/O2YW3ZC2JBI5AT6LEDDUVC6NEF/events.json","paper":"https://pith.science/paper/O2YW3ZC2"},"agent_actions":{"view_html":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF","download_json":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF.json","view_paper":"https://pith.science/paper/O2YW3ZC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2359&json=true","fetch_graph":"https://pith.science/api/pith-number/O2YW3ZC2JBI5AT6LEDDUVC6NEF/graph.json","fetch_events":"https://pith.science/api/pith-number/O2YW3ZC2JBI5AT6LEDDUVC6NEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF/action/storage_attestation","attest_author":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF/action/author_attestation","sign_citation":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF/action/citation_signature","submit_replication":"https://pith.science/pith/O2YW3ZC2JBI5AT6LEDDUVC6NEF/action/replication_record"}},"created_at":"2026-05-18T01:09:07.299856+00:00","updated_at":"2026-05-18T01:09:07.299856+00:00"}