{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:FE6JSTPGJJRGYD25RFHTUSHIJH","short_pith_number":"pith:FE6JSTPG","schema_version":"1.0","canonical_sha256":"293c994de64a626c0f5d894f3a48e849e4bf0d8ef1bedff7d5f836b1d4123002","source":{"kind":"arxiv","id":"1909.00332","version":1},"attestation_state":"computed","paper":{"title":"Set of independencies and Tutte polynomial of matroids over a domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Alessio Borz\\`i, Ivan Martino","submitted_at":"2019-09-01T06:29:29Z","abstract_excerpt":"In this work, we study matroids over a domain and several classical combinatorial and algebraic invariants related. We define their Grothendieck-Tutte polynomial $T_{\\mathcal{M}}(x,y)$, extending the definition given by Fink and Moci in 2016, and we show that such polynomial has the classical deletion-contraction property.\n  Moreover, we study the set of independencies for a realizable matroid over a domain, generalizing the definition of \\emph{poset of torsions} $Gr(\\mathcal{M})$ given by the second author in 2017. This is a union of identical simplicial posets as for (quasi-)arithmetic matro"},"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":"1909.00332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-01T06:29:29Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"d8a72f2f182a49ea442832884ac0d41adb38f883b947d5902ba181bc91cfc556","abstract_canon_sha256":"5f37e7dc39dcdd4269644a7612d10a116c726ed709f161717540d25e1cdab578"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:01:08.035554Z","signature_b64":"FwcocHpK9+Xgf6Z61L8lu0rAevvGynP1lmk2VjOFJVR8zYmic9IfRgYrsko3RshqIN0ZgQbsNcOc01zclVlKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293c994de64a626c0f5d894f3a48e849e4bf0d8ef1bedff7d5f836b1d4123002","last_reissued_at":"2026-07-05T00:01:08.035180Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:01:08.035180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Set of independencies and Tutte polynomial of matroids over a domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Alessio Borz\\`i, Ivan Martino","submitted_at":"2019-09-01T06:29:29Z","abstract_excerpt":"In this work, we study matroids over a domain and several classical combinatorial and algebraic invariants related. We define their Grothendieck-Tutte polynomial $T_{\\mathcal{M}}(x,y)$, extending the definition given by Fink and Moci in 2016, and we show that such polynomial has the classical deletion-contraction property.\n  Moreover, we study the set of independencies for a realizable matroid over a domain, generalizing the definition of \\emph{poset of torsions} $Gr(\\mathcal{M})$ given by the second author in 2017. This is a union of identical simplicial posets as for (quasi-)arithmetic matro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00332","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/1909.00332/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":"1909.00332","created_at":"2026-07-05T00:01:08.035232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.00332v1","created_at":"2026-07-05T00:01:08.035232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00332","created_at":"2026-07-05T00:01:08.035232+00:00"},{"alias_kind":"pith_short_12","alias_value":"FE6JSTPGJJRG","created_at":"2026-07-05T00:01:08.035232+00:00"},{"alias_kind":"pith_short_16","alias_value":"FE6JSTPGJJRGYD25","created_at":"2026-07-05T00:01:08.035232+00:00"},{"alias_kind":"pith_short_8","alias_value":"FE6JSTPG","created_at":"2026-07-05T00:01:08.035232+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/FE6JSTPGJJRGYD25RFHTUSHIJH","json":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH.json","graph_json":"https://pith.science/api/pith-number/FE6JSTPGJJRGYD25RFHTUSHIJH/graph.json","events_json":"https://pith.science/api/pith-number/FE6JSTPGJJRGYD25RFHTUSHIJH/events.json","paper":"https://pith.science/paper/FE6JSTPG"},"agent_actions":{"view_html":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH","download_json":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH.json","view_paper":"https://pith.science/paper/FE6JSTPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.00332&json=true","fetch_graph":"https://pith.science/api/pith-number/FE6JSTPGJJRGYD25RFHTUSHIJH/graph.json","fetch_events":"https://pith.science/api/pith-number/FE6JSTPGJJRGYD25RFHTUSHIJH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH/action/storage_attestation","attest_author":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH/action/author_attestation","sign_citation":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH/action/citation_signature","submit_replication":"https://pith.science/pith/FE6JSTPGJJRGYD25RFHTUSHIJH/action/replication_record"}},"created_at":"2026-07-05T00:01:08.035232+00:00","updated_at":"2026-07-05T00:01:08.035232+00:00"}