Year: 2011
Type: article
Abstract: Let O_n and C_n be the semigroup of all order-preserving transformations and of all order-preserving and order-decreasing transformations on the finite set X_n={1,2,\ldots ,n}, respectively. Let \fix (\alpha )={x\in X_n:x\alpha =x} for any transformation \alpha. In this paper, for any Y\subseteq X_n, we find the cardinalities of the sets O_{n,Y}={\alpha\in O_n:\fix (\alpha)=Y} and C_{n,Y}={\alpha\in C_n: \fix (\alpha )=Y}. Moreover, we find the numbers of transformations of O_n and C_n with r fixed points.
Source: TURKISH JOURNAL OF MATHEMATICS
DOI: 10.3906/mat-1010-432
Authors: GONCA AYIK, HAYRULLAH AYIK, METİN KOÇ
Institutions: Adıyaman University, Cukurova University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2151427033