By Bashir Ali and others

Let *\mathcal{CP}_n* be the semigroup of partial contraction mappings on *[n]=\{1,2,\ldots,n\}* and let *\mathcal{OCP}_n* and *\mathcal{ORCP}_n* be its subsemigroups consisting of all order-preserving and of all order-preserving or order-reversing, partial contraction mappings, respectively. In this paper we obtain the rank of the two semigroups, *\mathcal{OCP}_n* and *\mathcal{ORCP}_n*, respectively.

June 30, 2022

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On the Ranks of Semigroup of Order-preserving or Order-reversing Partial Contraction Mappings on a Finite Chain

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