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Idempotent rank in the endomorphism monoid of a non-uniform partition (1504.02520v1)
Published 9 Apr 2015 in math.GR
Abstract: We calculate the rank and idempotent rank of the semigroup $E(X,P)$ generated by the idempotents of the semigroup $T(X,P)$, which consists of all transformations of the finite set $X$ preserving a non-uniform partition $P$. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.