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A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

The Euler numbers, also called the secant numbers or zig numbers, are defined for |x|<pi/2 by sechx-1=-(E_1^*x^2)/(2!)+(E_2^*x^4)/(4!)-(E_3^*x^6)/(6!)+... (1) ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

The Hermite polynomials H_n(x) are set of orthogonal polynomials over the domain (-infty,infty) with weighting function e^(-x^2), illustrated above for n=1, 2, 3, and 4. ...

The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u,k), dn(u,k), and sn(u,k), where k is known as the elliptic ...

Let x=[a_0;a_1,...]=a_0+1/(a_1+1/(a_2+1/(a_3+...))) (1) be the simple continued fraction of a "generic" real number x, where the numbers a_i are the partial denominator. ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...