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Stanley and Wilf conjectured (Bona 1997, Arratia 1999), that for every permutation pattern sigma, there is a constant c(sigma)<infty such that for all n, ...

The superfactorial of n is defined by Pickover (1995) as n$=n!^(n!^(·^(·^(·^(n!)))))_()_(n!). (1) The first two values are 1 and 4, but subsequently grow so rapidly that 3$ ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

A vector space with a T2-space topology such that the operations of vector addition and scalar multiplication are continuous. The interesting examples are ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

A truncated polyhedron is a polyhedron with truncated faces, given by the Schläfli symbol t{p; q}. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...