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Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

The forward difference is a finite difference defined by Deltaa_n=a_(n+1)-a_n. (1) Higher order differences are obtained by repeated operations of the forward difference ...

A prime magic square is a magic square consisting only of prime numbers (although the number 1 is sometimes allowed in such squares). The left square is the 3×3 prime magic ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

A Room square (named after T. G. Room) of order n (for n even) is an arrangement in an (n-1)×(n-1) square matrix of n objects such that each cell is either empty or holds ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

The constants lambda_(m,n)=inf_(r in R_(m,n))sup_(x>=0)|e^(-x)-r(x)|, where r(x)=(p(x))/(q(x)), p and q are mth and nth order polynomials, and R_(m,n) is the set of all ...

The unique magic square of order three. The Lo Shu is an associative magic square, but not a panmagic square.