{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CRWG7CVP4PNCYCJ26BXYDQD7M3","short_pith_number":"pith:CRWG7CVP","schema_version":"1.0","canonical_sha256":"146c6f8aafe3da2c093af06f81c07f66dfdd2b154af501ae3ea35cd7d3786f0f","source":{"kind":"arxiv","id":"1509.09210","version":1},"attestation_state":"computed","paper":{"title":"On trees with the same restricted U-polynomial and the Prouhet-Tarry-Escott problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anna de Mier, Jos\\'e Aliste-Prieto, Jos\\'e Zamora","submitted_at":"2015-09-30T15:10:51Z","abstract_excerpt":"This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same $U$-polynomial (or, equivalently, the same chromatic symmetric function). We consider the $U_k$-polynomial, which is a restricted version of $U$-polynomial, and construct with the help of solutions of the Prouhet-Tarry-Escott problem, non-isomorphic trees with the same $U_k$-polynomial for any given $k$. By doing so, we also find a new class of trees that are distinguished by the $U$-polynomial up to isomorphism."},"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":"1509.09210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-30T15:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"8dcfd8f8a8862e1363422bfbd3f7143cf6473f23502ab459ecced80fd12d5254","abstract_canon_sha256":"59cf818bb668f6ec2062e021401954008198940238114e74bb33657252eb5ce4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:26.816730Z","signature_b64":"jJxyIyF8whF9dGnqEdiEWY/MgYFJwWI5Xs5ab84Tuv0FWwT3iU1bv6tBmrBROzef0TPA67kxDfhSNdB3KhfpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"146c6f8aafe3da2c093af06f81c07f66dfdd2b154af501ae3ea35cd7d3786f0f","last_reissued_at":"2026-05-18T01:31:26.816094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:26.816094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On trees with the same restricted U-polynomial and the Prouhet-Tarry-Escott problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anna de Mier, Jos\\'e Aliste-Prieto, Jos\\'e Zamora","submitted_at":"2015-09-30T15:10:51Z","abstract_excerpt":"This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same $U$-polynomial (or, equivalently, the same chromatic symmetric function). We consider the $U_k$-polynomial, which is a restricted version of $U$-polynomial, and construct with the help of solutions of the Prouhet-Tarry-Escott problem, non-isomorphic trees with the same $U_k$-polynomial for any given $k$. By doing so, we also find a new class of trees that are distinguished by the $U$-polynomial up to isomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09210","kind":"arxiv","version":1},"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":"1509.09210","created_at":"2026-05-18T01:31:26.816195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.09210v1","created_at":"2026-05-18T01:31:26.816195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09210","created_at":"2026-05-18T01:31:26.816195+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRWG7CVP4PNC","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRWG7CVP4PNCYCJ2","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRWG7CVP","created_at":"2026-05-18T12:29:17.054201+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/CRWG7CVP4PNCYCJ26BXYDQD7M3","json":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3.json","graph_json":"https://pith.science/api/pith-number/CRWG7CVP4PNCYCJ26BXYDQD7M3/graph.json","events_json":"https://pith.science/api/pith-number/CRWG7CVP4PNCYCJ26BXYDQD7M3/events.json","paper":"https://pith.science/paper/CRWG7CVP"},"agent_actions":{"view_html":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3","download_json":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3.json","view_paper":"https://pith.science/paper/CRWG7CVP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.09210&json=true","fetch_graph":"https://pith.science/api/pith-number/CRWG7CVP4PNCYCJ26BXYDQD7M3/graph.json","fetch_events":"https://pith.science/api/pith-number/CRWG7CVP4PNCYCJ26BXYDQD7M3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3/action/storage_attestation","attest_author":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3/action/author_attestation","sign_citation":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3/action/citation_signature","submit_replication":"https://pith.science/pith/CRWG7CVP4PNCYCJ26BXYDQD7M3/action/replication_record"}},"created_at":"2026-05-18T01:31:26.816195+00:00","updated_at":"2026-05-18T01:31:26.816195+00:00"}