Associative polynomial functions over bounded distributive lattices

Marichal, Jean-Luc; Couceiro, Miguel

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

Number

Publisher

Springer

Pages

1-8

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