Clonoids of Boolean functions with a monotone or discriminator source clone
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911935397625856 |
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| author | Lehtonen, Erkko |
| author_facet | Lehtonen, Erkko |
| contents | Extending Sparks's theorem, we determine the cardinality of the lattice of $(C_1,C_2)$-clonoids of Boolean functions in the cases where the target clone $C_2$ is the clone of projections. Moreover, we explicitly describe the $(C_1,C_2)$-clonoids of Boolean functions in the cases where the source clone $C_1$ is one of the four clones of monotone functions or contains the discriminator function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clonoids of Boolean functions with a monotone or discriminator source clone Lehtonen, Erkko Combinatorics Rings and Algebras Extending Sparks's theorem, we determine the cardinality of the lattice of $(C_1,C_2)$-clonoids of Boolean functions in the cases where the target clone $C_2$ is the clone of projections. Moreover, we explicitly describe the $(C_1,C_2)$-clonoids of Boolean functions in the cases where the source clone $C_1$ is one of the four clones of monotone functions or contains the discriminator function. |
| title | Clonoids of Boolean functions with a monotone or discriminator source clone |
| topic | Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2405.01164 |