References of "Szendrei, Ágnes"
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See detailCommuting polynomial operations of distributive lattices
Behrisch, Mike; Couceiro, Miguel UL; Kearnes, Keith A. et al

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.

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See detailPartial orders induced by quasilinear clones
Lehtonen, Erkko UL; Szendrei, Ágnes

in Czermak, J.; Dorfer, G.; Eigenthaler, G. (Eds.) et al Proceedings of the Salzburg Conference 2011 (AAA81) (2012)

We find sufficient conditions for a subclone C of Burle's clone and for a subclone of the polynomial clone of a finite semimodule to have the property that the associated C-minor partial order has finite ... [more ▼]

We find sufficient conditions for a subclone C of Burle's clone and for a subclone of the polynomial clone of a finite semimodule to have the property that the associated C-minor partial order has finite principal ideals. We also prove that for these clones the C-minor partial order is universal for the class of countable partial orders whose principal ideals are finite. [less ▲]

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See detailClones with finitely many relative R-classes
Lehtonen, Erkko UL; Szendrei, Ágnes

in Algebra Universalis (2011), 65(2), 109-159

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other ... [more ▼]

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the clones for which there are only finitely many relative R-classes. [less ▲]

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See detailThe submaximal clones on the three-element set with finitely many relative R-classes
Lehtonen, Erkko UL; Szendrei, Ágnes

in Discussiones Mathematicae. General Algebra and Applications (2010), 30(1), 7-33

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other ... [more ▼]

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes. [less ▲]

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See detailEquivalence of operations with respect to discriminator clones
Lehtonen, Erkko UL; Szendrei, Ágnes

in Discrete Mathematics (2009), 309(4), 673-685

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of ... [more ▼]

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In this paper we prove that if C is a discriminator clone on a finite set, then there are only finitely many C-equivalence classes. Moreover, we show that the smallest discriminator clone is minimal with respect to this finiteness property. For discriminator clones of Boolean functions we explicitly describe the associated equivalence relations. [less ▲]

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