Let $\mathscr {R}$ be an $\mathrm {NIP}$ expansion of $(\mathbb {R},<,+)$ by closed subsets $\mathbb {R}^n$ and continuous functions $f : \mathbb {R}^m \to {R}^n$. Then is generically locally o-minimal. This follows from a more general theorem on expansions compact groups, which itself result quotients definable sets in $\aleph _1$-saturated structures equivalence relations are both externally ...

Abstract We consider a finite, connected and simple graph Γ that admits vertex-transitive group of automorphisms

Multicriteria sequencing problems with criteria ordered according to their importance are considered. Additional precedence and group technology constraints are imposed. We introduce a notion of a priority-generating vector function and suggest general techniques that form a base for the construction of polynomial time algorithms for numerous sequencing problems including all known polynomially...

In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.

For a large class of ordered trees it’s possible to take results at the root and move them to an arbitrary vertex (the mutator) or to a leaf of the tree. This is the uplift principle. If you also sort by height and record the results in matrix form you end up with one or more elements of a group of infinite lower triangular matrices called the Riordan group. The main tools used are generating f...

Let P be a finite ordered set, and let J(P ) be the distributive lattice of order ideals of P . The covering relations of J(P ) are naturally associated with elements of P ; in this way, each element of P defines an involution on the set J(P ). Let Γ(P ) be the permutation group generated by these involutions. We show that if P is connected then Γ(P ) is either the alternating or the symmetric ...