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March 17, 2026Open Access

On the semigroups of order-preserving and orientation-preserving full contraction mappings on a finite chain

Puntos clave

The aim is to analyze the properties of semigroups of order-preserving and orientation-preserving transformations on finite chains.
Define the semigroups of order-preserving and orientation-preserving contraction mappings.
Calculate the cardinalities of several subsemigroups.
Identify minimal generating sets for these semigroups.
Determine the number of idempotents in the order-decreasing transformation semigroup.
Cardinalities of OPCTn and OPDCTn are established.
Minimal generating sets for the semigroups are identified.
The count of idempotents in OPDCTn is determined.

Resumen

Let OPCTn (OCTn) denote the semigroup consisting of all orientation-preserving (order-preserving) full contraction mappings on the finite chain Xn = 1 < ··· < n, and let OPDCTn (ODCTn) denote the subsemigroup of OPCTn (OCTn) consisting of all order-decreasing transformations. The purpose of this paper is to determine the cardinalities of OPCTn, OPDCTn, N (ODCTn), and N (OPDCTn), and to identify generating sets of minimal size, thereby determining their ranks. Moreover, the number of idempotents of OPDCTn is determined.

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