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Let G be a permutation group on a set Omega and x be an element of Omega. Then G_x={g in G:g(x)=x} (1) is called the stabilizer of x and consists of all the permutations of G ...

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

The term two-sided ideal is used in noncommutative rings to denote a subset that is both a right ideal and a left ideal. In commutative rings, where right and left are ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

An ideal is a subset I of elements in a ring R that forms an additive group and has the property that, whenever x belongs to R and y belongs to I, then xy and yx belong to I. ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

A board is a subset of the polygons determined by a number of (usually regularly spaced and oriented) lines. These polygons form the spaces on which "pieces" can be placed ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a floating-point representation is an unencoded member of a floating-point format which represents either ...