Reference : Associative polynomial functions over bounded distributive lattices
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/2814
Associative polynomial functions over bounded distributive lattices
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mar-2011
Order : A Journal on the Theory of Ordered Sets and its Applications
Springer
28
1
1-8
Yes
International
0167-8094
1572-9273
[en] bounded distributive lattice ; polynomial function ; associativity ; idempotency ; range-idempotency ; functional equation
[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.
http://hdl.handle.net/10993/2814
10.1007/s11083-010-9150-8
http://arXiv.org/abs/0902.2323

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