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  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations
JF  - Semigroup forum
N2  - We characterize the maximal regular subsemigroups of the ideals of the semigroup of all order-preserving transformations as well as of the semigroup of all order-preserving or order-reversing transformations on a finite ordered set.
KW  - Transformation semigroups
KW  - Regular semigroups
KW  - Order-preserving transformations
KW  - Order-reversing transformations
KW  - Maximal subsemigroups
Y1  - 2011
U6  - https://doi.org/10.1007/s00233-010-9272-8
SN  - 0037-1912
VL  - 82
IS  - 1
SP  - 172
EP  - 180
PB  - Springer
CY  - New York
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  -