{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7FQWPJUSUW4MEMWY6DTP74I7W7","short_pith_number":"pith:7FQWPJUS","schema_version":"1.0","canonical_sha256":"f96167a692a5b8c232d8f0e6fff11fb7d7ce3b97387c9eaf80e5b7fa3acd9443","source":{"kind":"arxiv","id":"1112.4901","version":4},"attestation_state":"computed","paper":{"title":"A supercharacter table decomposition via power-sum symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nantel Bergeron, Nathaniel Thiem","submitted_at":"2011-12-21T01:11:12Z","abstract_excerpt":"We give an $AB$-factorization of the supercharacter table of the group of $n\\times n$ unipotent upper triangular matrices over $\\FF_q$, where $A$ is a lower-triangular matrix with entries in $\\ZZ[q]$ and $B$ is a unipotent upper-triangular matrix with entries in $\\ZZ[q^{-1}]$. To this end we introduce a $q$ deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommutative variables. The factorization is obtain from the transition matrices between the supercharacter basis, the $q$-power-sum basis and the superclass basis. This is similar to the decomposition of t"},"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":"1112.4901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-21T01:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"d89e18f3e2a7c1efff25cf64739576b1b51c23de361ac9f7aa27e03b0e7e01a4","abstract_canon_sha256":"844983b6b9baf384a94dfd72c3076db0ed76cf4c2bf3dc84fa048d474af6d940"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:32.949730Z","signature_b64":"9/S1L9ZYOHpFOgdtjm/RtQ8sh6Wwbov7Lm05nxYffpi9hmz0XRYa9irSzCnWiQIijHDQTGvqWaxHLRdB6Qw1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f96167a692a5b8c232d8f0e6fff11fb7d7ce3b97387c9eaf80e5b7fa3acd9443","last_reissued_at":"2026-05-18T03:20:32.948675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:32.948675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A supercharacter table decomposition via power-sum symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nantel Bergeron, Nathaniel Thiem","submitted_at":"2011-12-21T01:11:12Z","abstract_excerpt":"We give an $AB$-factorization of the supercharacter table of the group of $n\\times n$ unipotent upper triangular matrices over $\\FF_q$, where $A$ is a lower-triangular matrix with entries in $\\ZZ[q]$ and $B$ is a unipotent upper-triangular matrix with entries in $\\ZZ[q^{-1}]$. To this end we introduce a $q$ deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommutative variables. The factorization is obtain from the transition matrices between the supercharacter basis, the $q$-power-sum basis and the superclass basis. This is similar to the decomposition of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4901","kind":"arxiv","version":4},"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":"1112.4901","created_at":"2026-05-18T03:20:32.948818+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4901v4","created_at":"2026-05-18T03:20:32.948818+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4901","created_at":"2026-05-18T03:20:32.948818+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FQWPJUSUW4M","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FQWPJUSUW4MEMWY","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FQWPJUS","created_at":"2026-05-18T12:26:22.705136+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/7FQWPJUSUW4MEMWY6DTP74I7W7","json":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7.json","graph_json":"https://pith.science/api/pith-number/7FQWPJUSUW4MEMWY6DTP74I7W7/graph.json","events_json":"https://pith.science/api/pith-number/7FQWPJUSUW4MEMWY6DTP74I7W7/events.json","paper":"https://pith.science/paper/7FQWPJUS"},"agent_actions":{"view_html":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7","download_json":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7.json","view_paper":"https://pith.science/paper/7FQWPJUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4901&json=true","fetch_graph":"https://pith.science/api/pith-number/7FQWPJUSUW4MEMWY6DTP74I7W7/graph.json","fetch_events":"https://pith.science/api/pith-number/7FQWPJUSUW4MEMWY6DTP74I7W7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7/action/storage_attestation","attest_author":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7/action/author_attestation","sign_citation":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7/action/citation_signature","submit_replication":"https://pith.science/pith/7FQWPJUSUW4MEMWY6DTP74I7W7/action/replication_record"}},"created_at":"2026-05-18T03:20:32.948818+00:00","updated_at":"2026-05-18T03:20:32.948818+00:00"}