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Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...

A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, ...

A Lie algebra is said to be simple if it is not Abelian and has no nonzero proper ideals. Over an algebraically closed field of field characteristic 0, every simple Lie ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

The nth subfactorial (also called the derangement number; Goulden and Jackson 1983, p. 48; Graham et al. 2003, p. 1050) is the number of permutations of n objects in which no ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...