Abstract
We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite.
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Acknowledgements
The authors would like to thank Bruno Teheux for fruitful discussions and valuable remarks. This research is supported by the Internal Research Project R-AGR-0500 of the University of Luxembourg and the Luxembourg National Research Fund R-AGR-3080. The second author is also supported by the Hungarian National Foundation for Scientific Research, Grant No. K124749.
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Communicated by Mikhail Volkov.
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Devillet, J., Kiss, G. & Marichal, JL. Characterizations of quasitrivial symmetric nondecreasing associative operations. Semigroup Forum 98, 154–171 (2019). https://doi.org/10.1007/s00233-018-9980-z
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DOI: https://doi.org/10.1007/s00233-018-9980-z