Search Results for ""

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...

Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Let G be a group and theta n permutation of G. Then theta is an orthomorphism of G if the self-mapping nu of G defined by nu(x)=x^(-1)theta(x) is also an permutation of G.

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.