Combinatorial Results for Semigroups of Order-Preserving and A-Decreasing Finite Transformations

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Atıf İçin Kopyala

BUGAY L., YAĞCI M., AYIK H.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, cilt.42, sa.3, ss.921-932, 2019 (SCI-Expanded)

• 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 On(A) when 1 is an element of A.