Combinatorial results for order-preserving and order-decreasing transformations

Gonca AYIK

Makale detayları

Combinatorial results for order-preserving and order-decreasing transformations

Yazarlar:

Gonca AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.617-625

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747888

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

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.

 

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.

Makale detayları

Combinatorial results for order-preserving and order-decreasing transformations

Yazarlar:

Gonca AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.617-625

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747888

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Order-preserving transformations

order-decreasing transformations

nilpotent

Catalan number

Sayı

Makale detayları

Combinatorial results for order-preserving and order-decreasing transformations

Yazarlar: Gonca AYIK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.617-625

Belge Tipi: Makale

Yayın Tarihi: 3/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747888

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Order-preserving transformations

order-decreasing transformations

nilpotent

Catalan number

Sayı

Yazarlar:

Gonca AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.617-625

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747888

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098