On the number of clonoids

2018/10/29 by Sparks, Athena
#08A40 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1810.12422

Abstract

A clonoid is a set of finitary functions from a set A to a set B that is closed under taking minors. Hence clonoids are generalizations of clones. By a classical result of Post, there are only countably many clones on a 2-element set. In contrast to that, we present continuum many clonoids for A = B = \0,1\. More generally, for any finite set A and any 2-element algebra B, we give the cardinality of the set of clonoids from A to B that are closed under the operations of B.

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