@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{DimitrovaFernandesKoppitz2012,
  author    = {Dimitrova, Ilinka and Fernandes, Vitor H. and Koppitz, J{\"o}rg},
  title     = {The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain},
  series = {Publicationes mathematicae},
  volume    = {81},
  journal   = {Publicationes mathematicae},
  number    = {1-2},
  publisher = {Institutum Mathematicum Universitatis Debreceniensis, Debreceni Tudom{\´a}nyegyetem Matematikai Int{\´e}zete},
  address   = {Debrecen},
  issn      = {0033-3883},
  doi       = {10.5486/PMD.2012.4897},
  pages     = {11 -- 29},
  year      = {2012},
  abstract  = {The study of the semigroups OPn, of all orientation-preserving transformations on an n-element chain, and ORn, of all orientation-preserving or orientation-reversing transformations on an n-element chain, has began in [17] and [5]. In order to bring more insight into the subsemigroup structure of OPn and ORn, we characterize their maximal subsemigroups.},
  language  = {en}
}