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


BUGAY L. , YAĞCI M. , AYIK H.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, cilt.42, ss.921-932, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s40840-017-0529-1
  • Dergi Adı: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Sayfa Sayıları: ss.921-932

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.