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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

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/0902.2323
Date
2011
Journal name
Order
Volume
28
Number
1
Publisher
Springer
Pages
1-8
Publication identifier
http://dx.doi.org/10.1007/s11083-010-9150-8
Metadata
Show full item record
Author(s)
Marichal, Jean-Luc
Couceiro, Miguel
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 / Keywords
Bounded distributive lattice; Polynomial function; Associativity; Idempotency; Range-idempotency; Functional equation

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