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A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

The Kepler-Poinsot polyhedra are four regular polyhedra which, unlike the Platonic solids, contain intersecting facial planes. In addition, two of the four Kepler-Poinsot ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

An apodization function (also called a tapering function or window function) is a function used to smoothly bring a sampled signal down to zero at the edges of the sampled ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...