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The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

A bar graph is any plot of a set of data such that the number of data elements falling within one or more categories is indicated using a rectangle whose height or width is a ...

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

A function f(x) is said to be constructible if some algorithm F computes it, in binary, within volume O(f(x)), i.e., V_(F(x))=O(f(x)). Here, the volume V_(A(x)) is the ...

A definition assigns properties to some sort of mathematical object. For example, Euclid's Elements starts with a number of definitions, such as "a line is a breadthless ...

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

The size of a minimum edge cover in a graph G is known as the edge cover number of G, denoted rho(G). If a graph G has no isolated points, then nu(G)+rho(G)=|G|, where nu(G) ...

An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an n-flexagon is a Catalan number. By manipulating the ...