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A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...

Define the abundancy Sigma(n) of a positive integer n as Sigma(n)=(sigma(n))/n, (1) where sigma(n) is the divisor function. Then a pair of distinct numbers (k,m) is a ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

The alternating group graph AG_n is the undirected Cayley graph of the set of 2(n-2) generators of the alternating group A_n given by g_3^-, g_3^+, g_4^-, g_4^+, ..., g_n^-, ...

An antisymmetric (also called alternating) tensor is a tensor which changes sign when two indices are switched. For example, a tensor A^(x_1,...,x_n) such that ...