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arXiv · 1504.02520

Idempotent rank in the endomorphism monoid of a non-uniform partition

Igor Dolinka·James East·James D. Mitchell
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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.

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Igor Dolinka, James East, James D. Mitchell. 2015-04-09. Idempotent rank in the endomorphism monoid of a non-uniform partition. https://doi.org/10.1017/s0004972715000751

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