Article (Scientific journals)
Quasitrivial semigroups: characterizations and enumerations
Couceiro, Miguel; DEVILLET, Jimmy; MARICHAL, Jean-Luc
2019In Semigroup Forum, 98 (3), p. 472–498
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Keywords :
Quasitrivial semigroup; quasitrivial and commutative semigroup; quasitrivial and order-preserving semigroups; enumeration of quasitrivial semigroups; single-peaked ordering; single-plateaued weak ordering
Abstract :
[en] 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.
Disciplines :
Mathematics
Computer science
Author, co-author :
Couceiro, Miguel;  LORIA, CNRS - Inria Nancy Grand Est - Université de Lorraine
DEVILLET, Jimmy ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
MARICHAL, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Quasitrivial semigroups: characterizations and enumerations
Publication date :
June 2019
Journal title :
Semigroup Forum
ISSN :
1432-2137
Publisher :
Springer, New York, United States - New York
Volume :
98
Issue :
3
Pages :
472–498
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
Name of the research project :
R-AGR-0500 - IRP15 - MRO3 (20150301-20181231) - MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 06 February 2018

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