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

Authors

GONCA AYIKFollow
HAYRULLAH AYIKFollow

Author ORCID Identifier

GONCA AYIK: 0000-0003-2301-0669

HAYRULLAH AYIK: 0000-0001-7569-5597

Abstract

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

DOI

10.55730/1300-0098.3647

Keywords

Orientation-preserving, Order-decreasing, contraction, idempotent, nilpotent, rank

First Page

228

Last Page

239

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

AYIK, G, & AYIK, H (2026). On the semigroups of order-preserving and orientation-preserving full contraction mappings on a finite chain. Turkish Journal of Mathematics 50 (2): 228-239. https://doi.org/10.55730/1300-0098.3647