The Minor Order of Homomorphisms via Natural Dualities

in Order: A Journal on the Theory of Ordered Sets and its Applications (2022)

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in ... [more ▼]

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in terms of disjoint unions of dual partition lattices and investigate reconstruction problems for homomorphisms. [less ▲]

Conservative median algebras and semilattices

in Order: A Journal on the Theory of Ordered Sets and its Applications (2016), 33(1), 121-132

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median ... [more ▼]

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains. [less ▲]

Parametrized arity gap

in Order: A Journal on the Theory of Ordered Sets and its Applications (2013), 30(2), 557-572

We propose a parametrized version of arity gap. The parametrized arity gap gap(f,l) of a function f: Aⁿ → B measures the minimum decrease in the number of essential variables of f when l consecutive ... [more ▼]

We propose a parametrized version of arity gap. The parametrized arity gap gap(f,l) of a function f: Aⁿ → B measures the minimum decrease in the number of essential variables of f when l consecutive identifications of pairs of essential variables are performed. We determine gap(f,l) for an arbitrary function f and a positive integer l. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions. [less ▲]

Commuting polynomial operations of distributive lattices

in Order: A Journal on the Theory of Ordered Sets and its Applications (2012), 29(2), 245-269

We describe which pairs of distributive lattice polynomial operations commute.

On the homomorphism order of labeled posets

in Order: A Journal on the Theory of Ordered Sets and its Applications (2011), 28(2), 251-265

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the ... [more ▼]

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined. [less ▲]

Aggregation on finite ordinal scales by scale independent functions

in Order: A Journal on the Theory of Ordered Sets and its Applications (2004), 21(2), 155-180

We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have ... [more ▼]

We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲]