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Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...

What is the maximum number of queens that can be placed on an n×n chessboard such that no two attack one another? The answer is n-1 queens for n=2 or n=3 and n queens ...

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...

The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path ...

The sum I over all internal (circular) nodes of the paths from the root of an extended binary tree to each node. For example, in the tree above, the internal path length is ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...