Clonoids of Boolean functions with a monotone or discriminator source clone
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.01164
- arXiv:
- arXiv:2405.01164
- Bibcode:
- 2024arXiv240501164L
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Rings and Algebras
- E-Print:
- 38 pages