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An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

A labeled graph G=(V,E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n={1,2,...,n}, the number of ...

A k×n Latin rectangle is a k×n matrix with elements a_(ij) in {1,2,...,n} such that entries in each row and column are distinct. If k=n, the special case of a Latin square ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...