{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NOMSTJMUFE66K6MJXDNT5EO242","short_pith_number":"pith:NOMSTJMU","schema_version":"1.0","canonical_sha256":"6b9929a594293de57989b8db3e91dae68e09450e800c4601beb3368bff14cbf5","source":{"kind":"arxiv","id":"1510.02684","version":2},"attestation_state":"computed","paper":{"title":"A weighted sum over generalized Tesler matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Timothy Wilson","submitted_at":"2015-10-09T14:21:55Z","abstract_excerpt":"We generalize previous definitions of Tesler matrices to allow negative matrix entries and negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum over these matrices, which we call the Tesler function. Our interpretation uses a new class of symmetric function specializations which are defined by their values on Macdonald polynomials. As a result of this interpretation, we obtain a Tesler function expression for the Hall inner product $\\langle \\Delta_f e_n, p_{1^{n}}\\rangle$, where $\\Delta_f$ is the delta operator introduced by Bergeron, Garsia, Haiman, 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":"1510.02684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-09T14:21:55Z","cross_cats_sorted":[],"title_canon_sha256":"287661434d275b4ae3d0237ab33057fc9cac06a07c04a51d25118a7592f8d5f1","abstract_canon_sha256":"b9f14400c5a906796e0fec6d7965425ecc9f2edbbda9a67f327d5e660232ec99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:33.783506Z","signature_b64":"AKEajLL7SsG0GePaKs+9/59hFcCt0VKqW0ZMkblPydpxIL3H46NBXQaGjf5j4mpdcXb70OlRv2SEXEVRgoQCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b9929a594293de57989b8db3e91dae68e09450e800c4601beb3368bff14cbf5","last_reissued_at":"2026-05-18T01:30:33.782801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:33.782801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weighted sum over generalized Tesler matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Timothy Wilson","submitted_at":"2015-10-09T14:21:55Z","abstract_excerpt":"We generalize previous definitions of Tesler matrices to allow negative matrix entries and negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum over these matrices, which we call the Tesler function. Our interpretation uses a new class of symmetric function specializations which are defined by their values on Macdonald polynomials. As a result of this interpretation, we obtain a Tesler function expression for the Hall inner product $\\langle \\Delta_f e_n, p_{1^{n}}\\rangle$, where $\\Delta_f$ is the delta operator introduced by Bergeron, Garsia, Haiman, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02684","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":"1510.02684","created_at":"2026-05-18T01:30:33.782903+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02684v2","created_at":"2026-05-18T01:30:33.782903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02684","created_at":"2026-05-18T01:30:33.782903+00:00"},{"alias_kind":"pith_short_12","alias_value":"NOMSTJMUFE66","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NOMSTJMUFE66K6MJ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NOMSTJMU","created_at":"2026-05-18T12:29:34.919912+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/NOMSTJMUFE66K6MJXDNT5EO242","json":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242.json","graph_json":"https://pith.science/api/pith-number/NOMSTJMUFE66K6MJXDNT5EO242/graph.json","events_json":"https://pith.science/api/pith-number/NOMSTJMUFE66K6MJXDNT5EO242/events.json","paper":"https://pith.science/paper/NOMSTJMU"},"agent_actions":{"view_html":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242","download_json":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242.json","view_paper":"https://pith.science/paper/NOMSTJMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02684&json=true","fetch_graph":"https://pith.science/api/pith-number/NOMSTJMUFE66K6MJXDNT5EO242/graph.json","fetch_events":"https://pith.science/api/pith-number/NOMSTJMUFE66K6MJXDNT5EO242/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242/action/storage_attestation","attest_author":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242/action/author_attestation","sign_citation":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242/action/citation_signature","submit_replication":"https://pith.science/pith/NOMSTJMUFE66K6MJXDNT5EO242/action/replication_record"}},"created_at":"2026-05-18T01:30:33.782903+00:00","updated_at":"2026-05-18T01:30:33.782903+00:00"}