Combinatorial results for order-preserving and order-decreasing transformations

被引：13

作者：

Ayik, Gonca ^{[1
]}

Ayik, Hayrullah ^{[2
]}

Koc, Metin ^{[1
]}

机构：

[1] Cukurova Univ, Dept Math, TR-01330 Adana, Turkey

[2] Adiyaman Univ, Dept Math, Adiyaman, Turkey

来源：

TURKISH JOURNAL OF MATHEMATICS | 2011年 / 35卷 / 04期

关键词：

Order-preserving transformations; order-decreasing transformations; nilpotent; Catalan number; SEMIGROUPS; IDEMPOTENTS;

D O I：

10.3906/mat-1010-432

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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,O-Y = {alpha is an element of O-n : Fix(alpha) = Y} and C-n,C-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.

引用

页码：617 / 625

页数：9

共 9 条

[1] The structure of elements in finite full transformation semigroups [J].