Combinatorial Results for Semigroups of Order-Preserving and A-Decreasing Finite Transformations
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, cilt.42, sa.3, ss.921-932, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 3
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s40840-017-0529-1
- Dergi Adı: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.921-932
- Çukurova Üniversitesi Adresli: Evet
Özet
For nN, let On be the semigroup of all order-preserving transformations on the finite chain Xn={1,...,n}, under its natural order. For any non-empty subset A of Xn, let On(A) and On+(A) be the subsemigroups of all order-preserving and A-decreasing, and of all order-preserving and A-increasing transformations on Xn, respectively. In this paper we obtain formulae for the number of elements and for the number of idempotents in On(A). Moreover, we show that On(A) contains a zero element if and only if 1A, and then we obtain the number of nilpotents in