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We prove that if S is a set of functions from a set A to itself, S is closedunder composition, and S contains all transpositions of A, then the action of Son Acan be recovered from the semigroup consisting of S together with itscompositionoperation. We also prove the analogous statement for clones.

Reconstruction theorems for semigroups of functions which contain all transpositions of a set and for clones with the same property