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A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

A transformation of a polynomial equation f(x)=0 which is of the form y=g(x)/h(x) where g and h are polynomials and h(x) does not vanish at a root of f(x)=0. The cubic ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

A vector space V with a ring structure and a vector norm such that for all v,W in V, ||vw||<=||v||||w||. If V has a multiplicative identity 1, it is also required that ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

The longstanding conjecture that the nonimaginary solutions E_n of zeta(1/2+iE_n)=0, (1) where zeta(z) is the Riemann zeta function, are the eigenvalues of an "appropriate" ...