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Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

A set T of integers is said to be recursively enumerable if it constitutes the range of a recursive function, i.e., if there exists a recursive function that can eventually ...

A number n such that sigma^2(n)=sigma(sigma(n))=2n, where sigma(n) is the divisor function is called a superperfect number. Even superperfect numbers are just 2^(p-1), where ...

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...

Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then ...

If a and n are relatively prime so that the greatest common divisor GCD(a,n)=1, then a^(lambda(n))=1 (mod n), where lambda is the Carmichael function.

A polynomial P(x) that, when evaluated over each x in the domain of definition, results in the same value. The simplest example is P(x)=c for x in R and c a constant.

A decahedron is a polyhedron having 10 faces. Examples include the 5-trapezohedron, augmented pentagonal prism (Johnson solid J_(52)), augmented tridiminished icosahedron ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

An object that is not superimposable on its mirror image is said to be dissymmetric. All asymmetric objects are dissymmetric, and an object with no improper rotation ...