- Turkish Journal of Mathematics
- Vol: 35 Issue: 4
- Combinatorial results for order-preserving and order-decreasing transformations
Combinatorial results for order-preserving and order-decreasing transformations
Authors : Gonca Ayik
Pages : 617-625
View : 6 | Download : 3
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let On and Cn be the semigroup of all order-preserving transformations and of all order-preserving and order-decreasing transformations on the finite set Xn={1,2,\ldots ,n}, respectively. Let \fix (a )={x\in Xn:xa =x} for any transformation a. In this paper, for any Y\subseteq Xn, we find the cardinalities of the sets On,Y={a\in On:\fix (a)=Y} and Cn,Y={a\in Cn: \fix (a )=Y}. Moreover, we find the numbers of transformations of On and Cn with r fixed points.Keywords : Order-preserving transformations, order-decreasing transformations, nilpotent, Catalan number