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Bisymmetric and quasitrivial operations: characterizations and enumerations

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Abstract

We investigate the class of bisymmetric and quasitrivial binary operations on a given set and provide various characterizations of this class as well as the subclass of bisymmetric, quasitrivial, and order-preserving binary operations. We also determine explicitly the sizes of these classes when the set is finite.

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Acknowledgements

The author thanks the reviewer for his/her quick and careful review and useful suggestions. He also thanks Miguel Couceiro, Jean-Luc Marichal, and Bruno Teheux for fruitful discussions and valuable remarks. The author is supported by the Luxembourg National Research Fund under the project PRIDE 15/10949314/GSM.

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  1. Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6, avenue de la Fonte, 4364, Esch-sur-Alzette, Luxembourg

    Jimmy Devillet

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Correspondence to Jimmy Devillet.

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Devillet, J. Bisymmetric and quasitrivial operations: characterizations and enumerations. Aequat. Math. 93, 501–526 (2019). https://doi.org/10.1007/s00010-019-00644-x

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  • DOI: https://doi.org/10.1007/s00010-019-00644-x

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