@article{MusunthiaKoppitz2017,
  author    = {Musunthia, Tiwadee and Koppitz, J{\"o}rg},
  title     = {Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set},
  series = {Forum mathematicum},
  volume    = {29},
  journal   = {Forum mathematicum},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0933-7741},
  doi       = {10.1515/forum-2015-0093},
  pages     = {971 -- 984},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{FernandesKoppitzMusunthia2019,
  author    = {Fernandes, Vitor H. and Koppitz, J{\"o}rg and Musunthia, Tiwadee},
  title     = {The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence},
  series = {Bulletin of the Malaysian Mathematical Sciences Society volume},
  volume    = {42},
  journal   = {Bulletin of the Malaysian Mathematical Sciences Society volume},
  number    = {5},
  publisher = {Malaysian mathematical sciences sciences soc},
  address   = {Pulau Punang},
  issn      = {0126-6705},
  doi       = {10.1007/s40840-017-0598-1},
  pages     = {2191 -- 2211},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{DimitrovaKoppitz2011,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations},
  series = {Semigroup forum},
  volume    = {82},
  journal   = {Semigroup forum},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0037-1912},
  doi       = {10.1007/s00233-010-9272-8},
  pages     = {172 -- 180},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}