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The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...

A (0,1)-matrix is an integer matrix in which each element is a 0 or 1. It is also called a logical matrix, binary matrix, relation matrix, or Boolean matrix. The number of ...

An alternating sign matrix is a matrix of 0s, 1s, and -1s in which the entries in each row or column sum to 1 and the nonzero entries in each row and column alternate in ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

The Hamming graph H(d,q), sometimes also denoted q^d, is the graph Cartesian product of d copies of the complete graph K_q. H(d,q) therefore has q^d vertices. H(d,q) has ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...