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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 ...

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 ...

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.

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

The deltoidal hexecontahedral graph is an Archimedean dual graph which is the skeleton of the deltoidal hexecontahedron as well as the rhombic hexecontahedron. It is ...