{"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. We study the cardinality of the set $\\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00781","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/2211.00781/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"}