IDEMPOTENT RANK IN THE ENDOMORPHISM MONOID OF A NONUNIFORM PARTITION
Igor Dolinka, James East, JAMES D. MITCHELL · Bulletin of the Australian Mathematical Society · 2015
We calculate the rank and idempotent rank of the semigroup ${\mathcal{E}}(X,{\mathcal{P}})$ generated by the idempotents of the semigroup ${\mathcal{T}}(X,{\mathcal{P}})$ which consists of all transformations of the finite set $X$ preserving a nonuniform partition ${\mathcal{P}}$ . We also classify and enumerate the idempotent generating sets of minimal possible size. This extends results of the first two authors in the uniform case.