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An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

The Clebsch graph, also known as the Greenwood-Gleason graph (Read and Wilson, 1998, p. 284) and illustrated above in a number of embeddings, is a strongly regular quintic ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

The Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...