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Associative Polynomial Functions over Bounded Distributive Lattices

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Abstract

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n ⩾ 1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.

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Authors and Affiliations

  1. Mathematics Research Unit, FSTC, University of Luxembourg, 6, rue Coudenhove-Kalergi, 1359, Luxembourg-Kirchberg, Luxembourg

    Miguel Couceiro & Jean-Luc Marichal

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  1. Miguel Couceiro
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  2. Jean-Luc Marichal
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Correspondence to Jean-Luc Marichal.

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Couceiro, M., Marichal, JL. Associative Polynomial Functions over Bounded Distributive Lattices. Order 28, 1–8 (2011). https://doi.org/10.1007/s11083-010-9150-8

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  • DOI: https://doi.org/10.1007/s11083-010-9150-8

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