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Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

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 ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

The word population has a number of distinct but closely related meanings in statistics. 1. A finite and actually existing group of objects which, although possibly large, ...

The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in S)(dimW) where ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...

Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can ...

The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n in Z and i in {0,1,2,3,...} there are ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...