{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T02:39:03Z","timestamp":1774406343382,"version":"3.50.1"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>Extending Sparks\u2019s theorem, we determine the cardinality of the lattice of [Formula: see text]-clonoids of Boolean functions for certain pairs [Formula: see text] of clones of essentially unary, linear, or [Formula: see text]- or [Formula: see text]-separating functions or semilattice operations. When such a [Formula: see text]-clonoid lattice is uncountable, the proof is in most cases based on exhibiting a countably infinite family of functions with the property that distinct subsets thereof always generate distinct [Formula: see text]-clonoids. In the cases when the lattice is finite, we enumerate the corresponding [Formula: see text]-clonoids. We also provide a summary of the cardinalities of [Formula: see text]-clonoid lattices of Boolean functions.<\/jats:p>","DOI":"10.1142\/s0218196725500419","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:32:09Z","timestamp":1760063529000},"page":"17-50","source":"Crossref","is-referenced-by-count":2,"title":["Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9255-5876","authenticated-orcid":false,"given":"Erkko","family":"Lehtonen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Khalifa University of Science and Technology, P.O. 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