Abstract.
In 1941, Post [9] presented the complete description of the countably many clones on 2 elements. The structure of the lattice of clones on finitely many (but more than 2) elements is more complex; in fact the lattice is of cardinality 2ℵ0. One approach is to study the monoidal intervals: the set of clones whose unary operations form a given monoid. One surprising fact is that for certain monoids, called collapsing, this interval contains just one clone. This article presents some collapsing monoids containing only constants and permutations.
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Fearnley, A., Rosenberg, I.G. Collapsing monoids containing permutations and constants. Algebra univers. 50, 149–156 (2003). https://doi.org/10.1007/s00012-003-1829-x
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DOI: https://doi.org/10.1007/s00012-003-1829-x