%0 Journal Article %T Quasitrivial semigroups: Characterizations and enumerations %+ Knowledge representation, reasonning (ORPAILLEUR) %+ Faculty of Science, Technology and Communication [Luxembourg] (FSTC) %A Couceiro, Miguel %A Devillet, Jimmy %A Marichal, Jean-Luc %< avec comité de lecture %@ 0037-1912 %J Semigroup Forum %I Springer Verlag %P 22 %8 2018 %D 2018 %Z Mathematics [math]Journal articles %X We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences. %G English %2 https://inria.hal.science/hal-01826868v1/document %2 https://inria.hal.science/hal-01826868v1/file/QuasitrivialSemigroups.pdf %L hal-01826868 %U https://inria.hal.science/hal-01826868