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If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...

The term "lobster" is used to refer either to a particular polyiamond or to a class of tree called a lobster graph. When referring to polyiamonds, the lobster is the ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

A polyabolo is an analog of the polyomino composed of n isosceles right triangles joined along edges of the same length. Polyaboloes are sometimes also called polytans ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

A polyform of 30-60-90 triangles. The name was coined by Ed Pegg, Jr. because of the 30-60-90 triangle's use in mechanical drawing and drafting. The Eternity puzzle is based ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

An n-he (a term coined by Brendan Owen) is a shape formed from a polyhex by removing half of each hexagon in such a way that the remaining pieces are connected (Clarke). The ...

A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...