On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals
Turkish Journal of Mathematics, cilt.50, sa.5, ss.913-932, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3774
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM), Academic Search Ultimate (EBSCO)
- Sayfa Sayıları: ss.913-932
- Anahtar Kelimeler: order-decreasing, Order-preserving, partial transformations, presentations, rank
- Çukurova Üniversitesi Adresli: Evet
Özet
In this paper, we consider the monoid ℛℕn of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid ℛℕn- of order-decreasing transformations. Our main aim is to give presentations for ℛℕn- and ℛℕ_n. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.