31 citations · 317 across the 62 of their papers we have counts for
7 papers · 2 filters
Self-commuting lattice polynomial functions
Miguel Couceiro, Erkko Lehtonen
We provide sufficient conditions for a lattice polynomial function to be self-commuting. We explicitly describe self-commuting polynomial functions over chains.
Invariant functionals on completely distributive lattices
Marta Cardin, Miguel Couceiro
In this paper we are interested in functionals defined on completely distributive lattices and which are invariant under mappings preserving {arbitrary} joins and meets. We prove t…
Finitely generated maximal partial clones and their intersections
Miguel Couceiro, Lucien Haddad
Let A be a finite non-singleton set. For |A|=2 we show that the partial clone consisting of all selfdual monotone partial functions on A is not finitely generated, while it is the…
The arity gap of polynomial functions over bounded distributive lattices
Miguel Couceiro, Erkko Lehtonen
Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to B is the minimum decrease in its essential arity when essential arguments of f are…
Galois connection for sets of operations closed under permutation, cylindrification and composition
Miguel Couceiro, Erkko Lehtonen
We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a G…
Associative polynomial functions over bounded distributive lattices
Miguel Couceiro, Jean-Luc Marichal
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 p…
Polynomial functions over bounded distributive lattices
Miguel Couceiro, Jean-Luc Marichal
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from pro…