29 citations · 162 across the 50 of their papers we have counts for
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The number of unary clones containing the permutations on an infinite set
Michael Pinsker
We calculate the number of unary clones (submonoids of the full transformation monoid) containing the permutations, on an infinite base set. It turns out that this number is quite…
Precomplete clones on infinite sets which are closed under conjugation
Michael Pinsker
We show that on an infinite set, there exist no other precomplete clones closed under conjugation except those which contain all permutations. Since on base sets of some infinite c…
Clones on infinite sets
Michael Pinsker
A clone on a set X is a set of finitary functions on X which contains the projections and which is closed under composition. The set of all clones on X forms a complete algebraic l…
Clones containing all almost unary functions
Michael Pinsker
Let X be an infinite set of regular cardinality. We determine all clones on X which contain all almost unary functions. It turns out that independently of the size of X, these clon…
The clone generated by the median functions
Michael Pinsker
Let X be a linearly ordered set of arbitrary size (finite or infinite). Natural functions on such a set one can define using the linear order include maximum, minimum and median fu…
Maximal clones on uncountable sets that include all permutations
Michael Pinsker
We first determine the maximal clones on a set X of infinite regular cardinality which contain all permutations but not all unary functions, extending a result of Heindorf's for co…