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Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a "reflected" code, or more ...

The Mertens constant B_1, also known as the Hadamard-de la Vallee-Poussin constant, prime reciprocal constant (Bach and Shallit 1996, p. 234), or Kronecker's constant ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

There are two problems commonly known as the subset sum problem. The first ("given sum problem") is the problem of finding what subset of a list of integers has a given sum, ...

1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 The Bell triangle, also called Aitken's array or the Peirce triangle (Knuth 2005, p. 28), is the number triangle obtained by beginning ...

A block is a maximal connected subgraph of a given graph G that has no articulation vertex (West 2000, p. 155). If a block has more than two vertices, then it is biconnected. ...

Branch and bound algorithms are a variety of adaptive partition strategies have been proposed to solve global optimization models. These are based upon partition, sampling, ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...