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The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

Consider a bivariate normal distribution in variables x and y with covariance rho=rho_(11)=<xy>-<x><y> (1) and an arbitrary function g(x,y). Then the expected value of the ...

Let sigma(m) be the divisor function of m. Then two numbers m and n are a quasiamicable pair if sigma(m)=sigma(n)=m+n+1. The first few are (48, 75), (140, 195), (1050, 1925), ...

A RAT-free ("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-free subset of ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...

A partial solution to the Erdős squarefree conjecture which states that the binomial coefficient (2n; n) is never squarefree for all sufficiently large n>=n_0. Sárkőzy (1985) ...