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From an earlier investigation we know that for certain digraphs $R$ and $S$, the relation \"$\\# {\\cal S}(G,R) \\leq \\# {\\cal S}(G,S)$ for all $G \\in \\mathfrak{ D }'$\" implies \"$\\# {\\cal H}(G,R) \\leq \\# {\\cal H}(G,S)$ for all $G \\in \\mathfrak{ D }'$\", where $\\mathfrak{ D }'$ is a subclass of digraphs. Now we ask for the inverse: For which digraphs $R, S$ and which subclasses $\\mathfrak{ D }"},"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":"2004.11653","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-24T11:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"5ec30eb4cfb0be9739b6f6f9e49acd8793c04625ac1fcb10be1e60013238c97f","abstract_canon_sha256":"03ae34342ec21150bfd005c41edc94dcadf8fbfcd6d75aa24d1d4bf0f80af71d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:50.865677Z","signature_b64":"4K/PDKvbEqC0zxUtqHNeXYxVe7pWlHf2zFznGLPDVvEyq4jBb17Q+gEqWa+FrGGTg7jp2uxPPX1BP21BhRGuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38f03da5f3d4d8619a452a24b3d8ffce8b68ded659cb48529da61894d2409a12","last_reissued_at":"2026-07-05T02:21:50.865331Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:50.865331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interdependencies of less-equal-relations between partial Lov\\'{a}sz-vectors of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frank a Campo","submitted_at":"2020-04-24T11:08:45Z","abstract_excerpt":"For digraphs $G$ and $H$, let ${\\cal H}(G,H)$ be the set of all homomorphisms from $G$ to $H$, and let ${\\cal S}(G,H)$ be the subset of those homomorphisms mapping all proper arcs in $G$ to proper arcs in $H$. From an earlier investigation we know that for certain digraphs $R$ and $S$, the relation \"$\\# {\\cal S}(G,R) \\leq \\# {\\cal S}(G,S)$ for all $G \\in \\mathfrak{ D }'$\" implies \"$\\# {\\cal H}(G,R) \\leq \\# {\\cal H}(G,S)$ for all $G \\in \\mathfrak{ D }'$\", where $\\mathfrak{ D }'$ is a subclass of digraphs. Now we ask for the inverse: For which digraphs $R, S$ and which subclasses $\\mathfrak{ D }"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.11653","kind":"arxiv","version":3},"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/2004.11653/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":"2004.11653","created_at":"2026-07-05T02:21:50.865391+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.11653v3","created_at":"2026-07-05T02:21:50.865391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.11653","created_at":"2026-07-05T02:21:50.865391+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDYD3JPT2TMG","created_at":"2026-07-05T02:21:50.865391+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDYD3JPT2TMGDGSF","created_at":"2026-07-05T02:21:50.865391+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDYD3JPT","created_at":"2026-07-05T02:21:50.865391+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/HDYD3JPT2TMGDGSFFISLHWH7Z2","json":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2.json","graph_json":"https://pith.science/api/pith-number/HDYD3JPT2TMGDGSFFISLHWH7Z2/graph.json","events_json":"https://pith.science/api/pith-number/HDYD3JPT2TMGDGSFFISLHWH7Z2/events.json","paper":"https://pith.science/paper/HDYD3JPT"},"agent_actions":{"view_html":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2","download_json":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2.json","view_paper":"https://pith.science/paper/HDYD3JPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.11653&json=true","fetch_graph":"https://pith.science/api/pith-number/HDYD3JPT2TMGDGSFFISLHWH7Z2/graph.json","fetch_events":"https://pith.science/api/pith-number/HDYD3JPT2TMGDGSFFISLHWH7Z2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2/action/storage_attestation","attest_author":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2/action/author_attestation","sign_citation":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2/action/citation_signature","submit_replication":"https://pith.science/pith/HDYD3JPT2TMGDGSFFISLHWH7Z2/action/replication_record"}},"created_at":"2026-07-05T02:21:50.865391+00:00","updated_at":"2026-07-05T02:21:50.865391+00:00"}