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The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

A double factorial prime is a prime number of the form n!!+/-1, where n!! is a double factorial. n!!-1 is prime for n=3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728, ... ...

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

A number of the form a_0+a_1zeta+...+a_(p-1)zeta^(p-1), where zeta=e^(2pii/p) is a de Moivre number and p is a prime number. Unique factorizations of cyclotomic integers fail ...

The polyhedral formula generalized to a surface of genus g, V-E+F=chi(g) where V is the number of polyhedron vertices, E is the number of polyhedron edges, F is the number of ...