Associative polynomial functions over bounded distributive lattices
Marichal, Jean-Luc; Couceiro, Miguel (2011), Associative polynomial functions over bounded distributive lattices, Order, 28, 1, p. 1-8. http://dx.doi.org/10.1007/s11083-010-9150-8
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0902.2323
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Abstract (EN)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.
Subjects / KeywordsBounded distributive lattice; Polynomial function; Associativity; Idempotency; Range-idempotency; Functional equation
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