Closure properties for relational systems with given endomorphism structure
A characterization of Sheffer functions by hyperidentities.
Classes of graphs definable by graph algebra identities or quasi-identities
Invariance groups of finite functions and orbit equivalence of permutation groups
Which subgroups of the symmetric group Sn 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 difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...
The minimal closed monoids for the Galois connection -
The minimal nontrivial endomorphism monoids of congruence lattices of algebras defined on a finite set are described. They correspond (via the Galois connection -) to the maximal nontrivial congruence lattices investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices .
Analytical enumeration of circulant graphs with prime-squared number of vertices.
Completeness criteria and invariants for operation and transformation algebras.
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