On the rank of transformation semigroup T(n,m)T(n,m)T_{(n,m)}

Kemal TOKER; Hayrullah AYIK

Makale detayları

On the rank of transformation semigroup T(n,m)T(n,m)T_{(n,m)}

Yazarlar:

Kemal TOKER | Hayrullah AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1970-1977

Belge Tipi:

Makale

Yayın Tarihi:

7/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745839

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Let TnTnT_{n} and SnSnS_{n} be the full transformation semigroup and the symmetric group   on Xn={1,…,n}Xn={1,…,n}X_{n}=\{1,\ldots,n\}, respectively.  For n,m∈Z+n,m∈Z+n,m\in \mathbb{Z}^{+} with m≤n−1m≤n−1m\le n-1 let   T(n,m)={α∈Tn:Xmα=Xm}.T(n,m)={α∈Tn:Xmα=Xm}.T_{(n,m)}=\{ \alpha \in T_{n} :  X_{m} \alpha = X_{m}\} .   In this paper we research generating sets and the rank of T(n,m)T(n,m)T_{(n,m)}. In particular, we prove  that   rank(T(n,m))=⎧⎪⎨⎪⎩2 if (n,m)=(2,1) or (3,2)3 if (n,m)=(3,1) or 4≤n and m=n−14 if 4≤n and 1≤m≤n−2.rank(T(n,m))={2 if (n,m)=(2,1) or (3,2)3 if (n,m)=(3,1) or 4≤n and m=n−14 if 4≤n and 1≤m≤n−2.rank(T_{(n,m)})=\left\{ \begin{array}{lll}   2 & \mbox{ if }\, (n,m)=(2,1) \mbox{ or }(3,2)\\   3 & \mbox{ if }\, (n,m)=(3,1) \mbox{ or } 4\leq n \mbox{ and } m=n-1\\   4 & \mbox{ if }\, 4\leq n \mbox{ and } 1\leq m\leq n-2.    \end{array}\right.   for 1≤m≤n−11≤m≤n−11\leq m\leq n-1.

Makale detayları

On the rank of transformation semigroup T(n,m)T(n,m)T_{(n,m)}

Yazarlar: Kemal TOKER | Hayrullah AYIK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1970-1977

Belge Tipi: Makale

Yayın Tarihi: 7/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745839

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Kemal TOKER | Hayrullah AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1970-1977

Belge Tipi:

Makale

Yayın Tarihi:

7/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745839

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098