8 papers
Higher-dimensional generalized quasiorders
Andrew Moorhead, Reinhard Pöschel
It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that a…
-preclones and the Galois connection -, Part I
Peter Jipsen, Erkko Lehtonen, Reinhard Pöschel
We consider -operations in which each argument is assigned a signum representing a "property" such as being order-preserving or order-reversing…
Generalized Quasiorders and the Galois Connection End-gQuord
Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radeleczki
Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relations) have the property that an -ary operation preserves , i.e., i…
Reflections and powers of multisorted minions
Erkko Lehtonen, Reinhard Pöschel
Classes of multisorted minions closed under extensions, reflections, and direct powers are considered from a relational point of view. As a generalization of a result of Barto, Opr…
Graph quasivarieties
Erkko Lehtonen, Reinhard Pöschel
Introduced by C. R. Shallon in 1979, graph algebras establish a useful connection between graph theory and universal algebra. This makes it possible to investigate graph varieties…
The lattice of congruence lattices of algebras on a finite set
Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radeleczki
The congruence lattices of all algebras defined on a fixed finite set ordered by inclusion form a finite atomistic lattice . We describe the atoms and coatoms. Each…
Permutation groups, pattern involvement, and Galois connections
Erkko Lehtonen, Reinhard Pöschel
There is a connection between permutation groups and permutation patterns: for any subgroup of the symmetric group and for any , the set of -permutatio…
Invariance groups of finite functions and orbit equivalence of permutation groups
Eszter K. Horváth, Géza Makay, Reinhard Pöschel +1
Which subgroups of the symmetric group S_n arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more…