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The multinomial coefficients (n_1,n_2,...,n_k)!=((n_1+n_2+...+n_k)!)/(n_1!n_2!...n_k!) (1) are the terms in the multinomial series expansion. In other words, the number of ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff ...

The Nørlund polynomial (note that the spelling Nörlund also appears in various publications) is a name given by Carlitz (1960) and Adelberg (1997) to the polynomial ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

A branch of mathematics which encompasses many diverse areas of minimization and optimization. Optimization theory is the more modern term for operations research. ...

Move a point Pi_0 along a line from an initial point to a final point. It traces out a line segment Pi_1. When Pi_1 is translated from an initial position to a final ...

A test for the primality of Fermat numbers F_n=2^(2^n)+1, with n>=2 and k>=2. Then the two following conditions are equivalent: 1. F_n is prime and (k/F_n)=-1, where (n/k) is ...