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When $\\mathcal{F}$ consists of all $r$-subsets of $[n]$, we shall simply write $W_{r,s}$ in place of $W_{r,s}^{\\mathcal{F}}$. In this paper we prove that the rank of the higher inclusion matrix $W_{r,s}$ over an arbitrary field $K$ is resilient. That is, if the size of $\\mathcal{F}$ is \"close\" to ${n \\choose r}$ then $\\mbox{rank}_{K}(W_{r,s}^{\\mathcal{F}}) = \\mbox{rank}_{K}(W_{r,s})"},"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":"1612.08124","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-24T01:50:25Z","cross_cats_sorted":[],"title_canon_sha256":"8c79a53cd3b7295d7e27ac7709ca4fc219b2096c1fe9f5810a578e3a739858f2","abstract_canon_sha256":"b8361128b0174e2584d9fb3609c788c159f86c9e620ff3e3c6e06bcea63c479a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:05.053629Z","signature_b64":"2uL38pcgL8fO5KiIY2yqJ/FhXiYFabBmVJrgo2mcMoZ8UQV3Vaj+0x8UQLHpOHgMFTCHb3duQhh+uP2UIK6+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08c2e9bab9040a1a6b4eedd4c4d7890817005b49cc570c90811baea18338ccda","last_reissued_at":"2026-05-18T00:34:05.052791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:05.052791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resilience of ranks of higher inclusion matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qing Xiang, Rafael Plaza","submitted_at":"2016-12-24T01:50:25Z","abstract_excerpt":"Let $n \\geq r \\geq s \\geq 0$ be integers and $\\mathcal{F}$ a family of $r$-subsets of $[n]$. 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