Combinatorial results for order-preserving and order-decreasing transformations

AYIK G., Ayik H., KOC M.

TURKISH JOURNAL OF MATHEMATICS, vol.35, no.4, pp.617-625, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.3906/mat-1010-432
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.617-625
  • Çukurova University Affiliated: Yes

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, ..., n}, respectively. Let Fix(alpha) = {x is an element of X(n) : x alpha = x} for any transformation alpha. In this paper; for any Y subset of X(n), we find the cardinalities of the sets O(n,Y) = {alpha is an element of O(n) : Fix(alpha) = Y} and C(n,Y) = {alpha is an element of C(n) : Fix(alpha) = Y}. Moreover; we find the numbers of transformations of O(n) and C(n) with r fixed points.