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The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. 1. ...

The number of "arrangements" in an ordering of n items is given by either a combination (order is ignored) or a permutation (order is significant). An ordering (or order) is ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

The "15 puzzle" is a sliding square puzzle commonly (but incorrectly) attributed to Sam Loyd. However, research by Slocum and Sonneveld (2006) has revealed that Sam Loyd did ...

The symbol +/- is used to denote a quantity which should be both added and subtracted, as in a+/-b. The symbol can be used to denote a range of uncertainty, or to denote a ...