Clonoids of Boolean functions with a monotone or discriminator source clone

2024/05/02 by Lehtonen, Erkko
#Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2405.01164

Abstract

Extending Sparks's theorem, we determine the cardinality of the lattice of (C₁,C₂)-clonoids of Boolean functions in the cases where the target clone C₂ is the clone of projections. Moreover, we explicitly describe the (C₁,C₂)-clonoids of Boolean functions in the cases where the source clone C₁ is one of the four clones of monotone functions or contains the discriminator function.

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