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Degen's eight-square identity is the incredible polynomial identity (1) found around 1818 by the Danish mathematician Ferdinand Degen (1766-1825). It was subsequently ...

The digraph intersection of two digraphs is the digraph whose vertex set (respectively, edge set) is the intersection of their vertex sets (respectively, edge sets). If n is ...

For even h, (1) (Nagell 1951, p. 176). Writing out symbolically, sum_(n=0)^h((-1)^nproduct_(k=0)^(n-1)(1-x^(h-k)))/(product_(k=1)^(n)(1-x^k))=product_(k=0)^(h/2-1)1-x^(2k+1), ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

The Cartesian product of a countable infinity of copies of the interval [0,1]. It can be denoted [0,1]^(aleph_0) or [0,1]^omega, where aleph_0 and omega are the first ...

A nonassociative algebra named after physicist Pascual Jordan which satisfies xy=yx (1) and (xx)(xy)=x((xx)y)). (2) The latter is equivalent to the so-called Jordan identity ...

A four-vector a_mu is said to be lightlike if its four-vector norm satisfies a_mua^mu=0. One should note that the four-vector norm is nothing more than a special case of the ...

For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...