Ranks of certain semigroups of transformations with idempotent complement whose restrictions belong to a given semigroup. (English) Zbl 1543.20068
Summary: For \(n \geq 2\), let \(P_n\), \(I_n\), \(T_n\), and \(S_n\) be the partial transformation semigroup, symmetric inverse semigroup, (full) transformation semigroup, and symmetric group on the set \(X_n = \{1, \dots, n\}\), respectively. In this paper, we find the ranks of certain subsemigroups of \(P_n\), \(I_n\), and \(T_n\) consisting of transformations with idempotent complement whose restrictions to the set \(X_m\) belong to the (possible) semigroup \(S_m\), \(I_m\), \(T_m\), or \(P_m\) for \(1 \leq m \leq n - 1\).
MSC:
| 20M20 | Semigroups of transformations, relations, partitions, etc. |
Keywords:
partial (full) transformation semigroup; symmetric inverse semigroup; symmetric group; idempotent; rankReferences:
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