@article{DimitrovaKoppitz2022,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range},
  series = {Communications in algebra},
  volume    = {50},
  journal   = {Communications in algebra},
  number    = {5},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0092-7872},
  doi       = {10.1080/00927872.2021.2000998},
  pages     = {2157 -- 2168},
  year      = {2022},
  abstract  = {Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.},
  language  = {en}
}
@article{TinpunKoppitz2016,
  author    = {Tinpun, Kittisak and Koppitz, J{\"o}rg},
  title     = {Generating sets of infinite full transformation semigroups with restricted range},
  series = {Acta scientiarum mathematicarum},
  volume    = {82},
  journal   = {Acta scientiarum mathematicarum},
  publisher = {Institutum Bolyaianum Universitatis Szegediensis},
  address   = {Szeged},
  issn      = {0001-6969},
  doi       = {10.14232/actasm-015-502-4},
  pages     = {55 -- 63},
  year      = {2016},
  abstract  = {In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.},
  language  = {en}
}