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Definability in the Substructure Ordering of Simple Graphs
For simple graphs, we investigate and seek to characterize the properties first-order definable by the induced subgraph relation. Let $${\mathcal{P}\mathcal{G}}$$PG denote the set of finiteExpand
Dichotomy for finite tournaments of mixed-type
  • A. Wires
  • Mathematics, Computer Science
  • Discret. Math.
  • 6 December 2015
TLDR
It is shown that if T c denotes the structure with all unary singleton relations in addition to the edge relation of the tournament, then it will follow that the constraint satisfaction problem with template T c satisfies the algebraic dichotomy conjecture. Expand
A quasi-Mal’cev condition with unexpected application
A quasi-Mal’cev condition for quasivarieties is established which in the case of locally finite quasivarieties forbids strongly abelian congruences and for varieties is equivalent to possessing aExpand
On supernilpotent algebras
We establish a characterization of supernilpotent Mal’cev algebras which generalizes the affine structure of abelian Mal’cev algebras and the recent characterization of 2-supernilpotent Mal’cevExpand
Complexity in Young's Lattice
We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the singleExpand
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On finite Taylor algebras
  • A. Wires
  • Computer Science, Mathematics
  • Int. J. Algebra Comput.
  • 20 December 2016
TLDR
The cyclic reduct of a finite Taylor algebra is introduced and a collapse of Mal’cev conditions is proved. Expand