{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:54KU7E4JAOXJXCQRM275KILDDQ","short_pith_number":"pith:54KU7E4J","schema_version":"1.0","canonical_sha256":"ef154f938903ae9b8a1166bfd521631c23906c55d00564f167d5d6eddbc653d2","source":{"kind":"arxiv","id":"1306.6910","version":2},"attestation_state":"computed","paper":{"title":"Segre embeddings, Hilbert series and Newcomb's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Marcel Morales (IF)","submitted_at":"2013-06-28T17:54:19Z","abstract_excerpt":"Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal $I$ in a polynomial ring a monomial ideal ${\\rm in}_\\prec I$, in some special situations the monomial ideal ${\\rm in}_\\prec I$ is square free. On the other hand given any monomial ideal $I$ of a polynomial ring $S$, we can define the toric $K[I]\\subset S$. In this paper we will study toric rings defined by Segre embeddings, we will prove that their $h-$ vectors coincides with the so called Simon Newcomb number's in probabilities and combinatorics. We solve the original questio"},"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":"1306.6910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-06-28T17:54:19Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"21736f38cb3ac234a8a0c37de67f79328028b97ce6df220ad643d98eb4ab7388","abstract_canon_sha256":"0f3969c353db9b07e475739b487065b9fc37b76d6add8b562a50b1cebdc29020"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:58.263894Z","signature_b64":"bypA6yOBWKTS7UqapfDAMzxUZ2ReWuxxgyhMSglBDoOSL1orwtFpurR2PKGHm473hd77MYHM9ey4cwHlTUivDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef154f938903ae9b8a1166bfd521631c23906c55d00564f167d5d6eddbc653d2","last_reissued_at":"2026-05-18T03:01:58.263271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:58.263271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Segre embeddings, Hilbert series and Newcomb's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Marcel Morales (IF)","submitted_at":"2013-06-28T17:54:19Z","abstract_excerpt":"Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal $I$ in a polynomial ring a monomial ideal ${\\rm in}_\\prec I$, in some special situations the monomial ideal ${\\rm in}_\\prec I$ is square free. On the other hand given any monomial ideal $I$ of a polynomial ring $S$, we can define the toric $K[I]\\subset S$. In this paper we will study toric rings defined by Segre embeddings, we will prove that their $h-$ vectors coincides with the so called Simon Newcomb number's in probabilities and combinatorics. We solve the original questio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6910","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":"1306.6910","created_at":"2026-05-18T03:01:58.263387+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.6910v2","created_at":"2026-05-18T03:01:58.263387+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6910","created_at":"2026-05-18T03:01:58.263387+00:00"},{"alias_kind":"pith_short_12","alias_value":"54KU7E4JAOXJ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"54KU7E4JAOXJXCQR","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"54KU7E4J","created_at":"2026-05-18T12:27:34.582898+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/54KU7E4JAOXJXCQRM275KILDDQ","json":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ.json","graph_json":"https://pith.science/api/pith-number/54KU7E4JAOXJXCQRM275KILDDQ/graph.json","events_json":"https://pith.science/api/pith-number/54KU7E4JAOXJXCQRM275KILDDQ/events.json","paper":"https://pith.science/paper/54KU7E4J"},"agent_actions":{"view_html":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ","download_json":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ.json","view_paper":"https://pith.science/paper/54KU7E4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.6910&json=true","fetch_graph":"https://pith.science/api/pith-number/54KU7E4JAOXJXCQRM275KILDDQ/graph.json","fetch_events":"https://pith.science/api/pith-number/54KU7E4JAOXJXCQRM275KILDDQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ/action/storage_attestation","attest_author":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ/action/author_attestation","sign_citation":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ/action/citation_signature","submit_replication":"https://pith.science/pith/54KU7E4JAOXJXCQRM275KILDDQ/action/replication_record"}},"created_at":"2026-05-18T03:01:58.263387+00:00","updated_at":"2026-05-18T03:01:58.263387+00:00"}