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In particular, we show for $\\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \\mathcal{E}(\\mathbf{M}_n) | =n!\\mathcal{L}_n(-1)+(n+1)^2$ where $\\mathcal{L}_n(x)$ is the Laguerre polynomial of degree $n$. We also study the following problem: Given a lattice $L$ of size $n$ and a set $S\\subseteq \\mathcal{E}(L)$ of size $m$, find the greatest lower bound ${\\large"},"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":"2211.00781","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2022-11-01T22:56:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"43a267150eea61cfa199d63b3de0b1f4eda44ed00333ae412482545e971a446e","abstract_canon_sha256":"3a8700319d27614a1ccc3c80f9756994de5e64826a7236d35c2412afb2ea28b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:12:34.803880Z","signature_b64":"9+7HKXKs+EgU3TFESDwPKyNBcFUcDdqiuTnQAU7m+gCfyacBz6CSUTQOrATLKaRJwKpKV0iHPdPYApT8go/vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501303262f6a5883cf5485ae8896ad48a47f29f11a2197223f88c637ebe3a9f3","last_reissued_at":"2026-07-05T05:12:34.803391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:12:34.803391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting and Computing Join-Endomorphisms in Lattices (Revisited)","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"cs.MA","authors_text":"Camilo Rueda, Carlos Pinz\\'on, Frank Valencia, Santiago Quintero, Sergio Ram\\'irez","submitted_at":"2022-11-01T22:56:47Z","abstract_excerpt":"Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. 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