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A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...

A minimal dominating set is a dominating set in a graph that is not a proper subset of any other dominating set. Every minimum dominating set is a minimal dominating set, but ...

An independent dominating set of a graph G is a set of vertices in G that is both an independent vertex set and a dominating set of G. The minimum size of an independent ...

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

A set S is said to be GCD-closed if GCD(x_i,x_j) in S for 1<=i,j<=n.

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

An independent edge set (also called a matching) of a graph G is a subset of the edges such that no two edges in the subset share a vertex of G (Skiena 1990, p. 219). The ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

A set A of integers is productive if there exists a partial recursive function f such that, for any x, the following holds: If the domain of phi_x is a subset of A, then f(x) ...