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We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols.\n  Let $A(i\\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\\eq"},"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":"1912.11230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-24T07:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"53f45f1244205289eb08bbf2dcd5a4f8e68a2e84623d538c669cd46459da6674","abstract_canon_sha256":"919f9efd2e117e262a6f23bed1c2113a72908cd0deef8a9b1eba32e3396c6a85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:59:13.860535Z","signature_b64":"gXXaJbXJiQnxcqMdRCd+fqenZQR1tjiIRau8dxfCsMdh9WL4/1YsyNLn2qua2/D1tH3Ou8Ds+fiL6oy/etxeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dfeba004c29eb43357acd7dd3ba19228741f3ccc5e51ef1c2471844d616fc0e","last_reissued_at":"2026-07-05T00:59:13.860168Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:59:13.860168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parity of transversals of Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darcy Best, Ian M. Wanless","submitted_at":"2019-12-24T07:02:26Z","abstract_excerpt":"We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \\bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols.\n  Let $A(i\\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\\eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.11230","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/1912.11230/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":"1912.11230","created_at":"2026-07-05T00:59:13.860229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.11230v1","created_at":"2026-07-05T00:59:13.860229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.11230","created_at":"2026-07-05T00:59:13.860229+00:00"},{"alias_kind":"pith_short_12","alias_value":"LX7LUACMFHVU","created_at":"2026-07-05T00:59:13.860229+00:00"},{"alias_kind":"pith_short_16","alias_value":"LX7LUACMFHVUGNL2","created_at":"2026-07-05T00:59:13.860229+00:00"},{"alias_kind":"pith_short_8","alias_value":"LX7LUACM","created_at":"2026-07-05T00:59:13.860229+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/LX7LUACMFHVUGNL2ZV65HOQZEK","json":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK.json","graph_json":"https://pith.science/api/pith-number/LX7LUACMFHVUGNL2ZV65HOQZEK/graph.json","events_json":"https://pith.science/api/pith-number/LX7LUACMFHVUGNL2ZV65HOQZEK/events.json","paper":"https://pith.science/paper/LX7LUACM"},"agent_actions":{"view_html":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK","download_json":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK.json","view_paper":"https://pith.science/paper/LX7LUACM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.11230&json=true","fetch_graph":"https://pith.science/api/pith-number/LX7LUACMFHVUGNL2ZV65HOQZEK/graph.json","fetch_events":"https://pith.science/api/pith-number/LX7LUACMFHVUGNL2ZV65HOQZEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK/action/storage_attestation","attest_author":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK/action/author_attestation","sign_citation":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK/action/citation_signature","submit_replication":"https://pith.science/pith/LX7LUACMFHVUGNL2ZV65HOQZEK/action/replication_record"}},"created_at":"2026-07-05T00:59:13.860229+00:00","updated_at":"2026-07-05T00:59:13.860229+00:00"}