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A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

An m-ary n-ic polynomial (i.e., a homogeneous polynomial with constant coefficients of degree n in m independent variables).

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

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 coordinate system which is similar to bispherical coordinates but having fourth-degree surfaces instead of second-degree surfaces for constant mu. The coordinates are given ...

The Bombieri p-norm of a polynomial Q(x)=sum_(i=0)^na_ix^i (1) is defined by [Q]_p=[sum_(i=0)^n(n; i)^(1-p)|a_i|^p]^(1/p), (2) where (n; i) is a binomial coefficient. The ...

Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...