{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GDXHPZ7I3KCWTRNMDJWAU3RJQK","short_pith_number":"pith:GDXHPZ7I","schema_version":"1.0","canonical_sha256":"30ee77e7e8da8569c5ac1a6c0a6e29829e52b1d6181db39740014dc56a5a7c36","source":{"kind":"arxiv","id":"2506.02985","version":1},"attestation_state":"computed","paper":{"title":"On 102-avoiding inversion sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heesung Shin, JiSun Huh, Sangwook Kim, Seunghyun Seo","submitted_at":"2025-06-03T15:22:03Z","abstract_excerpt":"In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schr\\\"{o}der paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled $F$-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In addition, we study inversion sequences avoiding 102 and another pattern of length 3, providing refi"},"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":"2506.02985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T15:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"3e5207a4faf38a5782e8878459b2b09a3cf40e443b532fc0411c201dd77384ae","abstract_canon_sha256":"fa948989b3376eea471d68b82889db467b50e1f59d99a565a0c4c47abf234310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:12.917083Z","signature_b64":"vNxJuovotOe3LvlZT/uUWxjToUp0otPHtde5PSeQHaX+4Z4CDs5WomBuyrbOb5GXdStf0aPsxXs7Je4FIApmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30ee77e7e8da8569c5ac1a6c0a6e29829e52b1d6181db39740014dc56a5a7c36","last_reissued_at":"2026-07-05T11:15:12.916610Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:12.916610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 102-avoiding inversion sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heesung Shin, JiSun Huh, Sangwook Kim, Seunghyun Seo","submitted_at":"2025-06-03T15:22:03Z","abstract_excerpt":"In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schr\\\"{o}der paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled $F$-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In addition, we study inversion sequences avoiding 102 and another pattern of length 3, providing refi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02985","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02985/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.02985","created_at":"2026-07-05T11:15:12.916668+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02985v1","created_at":"2026-07-05T11:15:12.916668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02985","created_at":"2026-07-05T11:15:12.916668+00:00"},{"alias_kind":"pith_short_12","alias_value":"GDXHPZ7I3KCW","created_at":"2026-07-05T11:15:12.916668+00:00"},{"alias_kind":"pith_short_16","alias_value":"GDXHPZ7I3KCWTRNM","created_at":"2026-07-05T11:15:12.916668+00:00"},{"alias_kind":"pith_short_8","alias_value":"GDXHPZ7I","created_at":"2026-07-05T11:15:12.916668+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/GDXHPZ7I3KCWTRNMDJWAU3RJQK","json":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK.json","graph_json":"https://pith.science/api/pith-number/GDXHPZ7I3KCWTRNMDJWAU3RJQK/graph.json","events_json":"https://pith.science/api/pith-number/GDXHPZ7I3KCWTRNMDJWAU3RJQK/events.json","paper":"https://pith.science/paper/GDXHPZ7I"},"agent_actions":{"view_html":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK","download_json":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK.json","view_paper":"https://pith.science/paper/GDXHPZ7I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02985&json=true","fetch_graph":"https://pith.science/api/pith-number/GDXHPZ7I3KCWTRNMDJWAU3RJQK/graph.json","fetch_events":"https://pith.science/api/pith-number/GDXHPZ7I3KCWTRNMDJWAU3RJQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK/action/storage_attestation","attest_author":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK/action/author_attestation","sign_citation":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK/action/citation_signature","submit_replication":"https://pith.science/pith/GDXHPZ7I3KCWTRNMDJWAU3RJQK/action/replication_record"}},"created_at":"2026-07-05T11:15:12.916668+00:00","updated_at":"2026-07-05T11:15:12.916668+00:00"}