Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones.
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| Title: | Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones. |
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| Authors: | Lehtonen, Erkko1 (AUTHOR) erkko.lehtonen@ku.ac.ae |
| Source: | International Journal of Algebra & Computation. Feb2026, Vol. 36 Issue 1, p17-50. 34p. |
| Subjects: | Boolean functions, Lattice theory, Linear operators, Cardinal numbers, Semilattices, Mathematical functions |
| Abstract: | Extending Sparks's theorem, we determine the cardinality of the lattice of (C 1 , C 2) -clonoids of Boolean functions for certain pairs (C 1 , C 2) of clones of essentially unary, linear, or 0 - or 1 -separating functions or semilattice operations. When such a (C 1 , C 2) -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 (C 1 , C 2) -clonoids. In the cases when the lattice is finite, we enumerate the corresponding (C 1 , C 2) -clonoids. We also provide a summary of the cardinalities of (C 1 , C 2) -clonoid lattices of Boolean functions. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 190554586 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lehtonen%2C+Erkko%22">Lehtonen, Erkko</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> erkko.lehtonen@ku.ac.ae</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Feb2026, Vol. 36 Issue 1, p17-50. 34p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+theory%22">Lattice theory</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+operators%22">Linear operators</searchLink><br /><searchLink fieldCode="DE" term="%22Cardinal+numbers%22">Cardinal numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Semilattices%22">Semilattices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Extending Sparks's theorem, we determine the cardinality of the lattice of (C 1 , C 2) -clonoids of Boolean functions for certain pairs (C 1 , C 2) of clones of essentially unary, linear, or 0 - or 1 -separating functions or semilattice operations. When such a (C 1 , C 2) -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 (C 1 , C 2) -clonoids. In the cases when the lattice is finite, we enumerate the corresponding (C 1 , C 2) -clonoids. We also provide a summary of the cardinalities of (C 1 , C 2) -clonoid lattices of Boolean functions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218196725500419 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 34 StartPage: 17 Subjects: – SubjectFull: Boolean functions Type: general – SubjectFull: Lattice theory Type: general – SubjectFull: Linear operators Type: general – SubjectFull: Cardinal numbers Type: general – SubjectFull: Semilattices Type: general – SubjectFull: Mathematical functions Type: general Titles: – TitleFull: Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lehtonen, Erkko IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181967 Numbering: – Type: volume Value: 36 – Type: issue Value: 1 Titles: – TitleFull: International Journal of Algebra & Computation Type: main |
| ResultId | 1 |
