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The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

The Hadwiger conjecture is a generalization of the four-color theorem which states that for any loopless graph G with h(G) the Hadwiger number and chi(G) the chromatic ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

A pair of positive integers (a_1,a_2) such that the equations a_1+a_2x=sigma(a_1)=sigma(a_2)(x+1) (1) have a positive integer solution x, where sigma(n) is the divisor ...

A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...

Let f(theta) be Lebesgue integrable and let f(r,theta)=1/(2pi)int_(-pi)^pif(t)(1-r^2)/(1-2rcos(t-theta)+r^2)dt (1) be the corresponding Poisson integral. Then almost ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

A statement which is rigorously known to be correct. A statement which is not true is called false, although certain statements can be proved to be rigorously undecidable ...

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...