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

AYIK G., AYIK H.

Turkish Journal of Mathematics, cilt.50, sa.2, ss.228-239, 2026 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.55730/1300-0098.3647
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.228-239
  • Anahtar Kelimeler: contraction, idempotent, nilpotent, order-decreasing, Orientation-preserving, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

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, OPCTₙ, 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.