TY  - JOUR
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
JF  - Bulletin of the Malaysian Mathematical Sciences Society volume
N2  - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
KW  - Transformation semigroups
KW  - Rank of semigroup
KW  - Idempotents
KW  - Order-preserving
KW  - Fence
KW  - Zig-zag order
Y1  - 2019
U6  - https://doi.org/10.1007/s40840-017-0598-1
SN  - 0126-6705
SN  - 2180-4206
VL  - 42
IS  - 5
SP  - 2191
EP  - 2211
PB  - Malaysian mathematical sciences sciences soc
CY  - Pulau Punang
ER  - 
TY  - JOUR
A1  - Musunthia, Tiwadee
A1  - Koppitz, Jörg
T1  - Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
JF  - Forum mathematicum
N2  - In this paper, we study the maximal subsemigroups of several semigroups of order-preserving transformations on the natural numbers and the integers, respectively. We determine all maximal subsemigroups of the monoid of all order-preserving injections on the set of natural numbers as well as on the set of integers. Further, we give all maximal subsemigroups of the monoid of all bijections on the integers. For the monoid of all order-preserving transformations on the natural numbers, we classify also all its maximal subsemigroups, containing a particular set of transformations.
KW  - Transformation semigroups
KW  - maximal subsemigroups
KW  - order-preserving mappings
Y1  - 2017
U6  - https://doi.org/10.1515/forum-2015-0093
SN  - 0933-7741
SN  - 1435-5337
VL  - 29
SP  - 971
EP  - 984
PB  - De Gruyter
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - Maximal subsemigroups containing a particular semigroup
JF  - Mathematica Slovaca
N2  - We characterize maximal subsemigroups of the monoid T(X) of all transformations on the set X = a"center dot of natural numbers containing a given subsemigroup W of T(X) such that T(X) is finitely generated over W. This paper gives a contribution to the characterization of maximal subsemigroups on the monoid of all transformations on an infinite set.
KW  - maximal subsemigroup
KW  - transformations on infinite set
Y1  - 2014
U6  - https://doi.org/10.2478/s12175-014-0280-0
SN  - 0139-9918
SN  - 1337-2211
VL  - 64
IS  - 6
SP  - 1369
EP  - 1380
PB  - De Gruyter
CY  - Warsaw
ER  - 
TY  - INPR
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - Maximal subsemigroups containing a particular semigroup
N2  - We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X = N of natural numbers containing a given subsemigroup W of T(X), where each element of a given set U is a generator of T(X) modulo W. This note continues the study of maximal subsemigroups of the monoid of all full transformations on an infinite set.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 8 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57465
ER  - 
TY  - THES
A1  - Musunthia, Tiwadee
T1  - On the study of varieties of rings with involution
Y1  - 2010
CY  - Potsdam
ER  -