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A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A set is said to be bounded from above if it has an upper bound. Consider the real numbers with their usual order. Then for any set M subset= R, the supremum supM exists (in ...

A set is said to be bounded from below if it has a lower bound. Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) ...

A finite, increasing sequence of integers {a_1,...,a_m} such that (a_i-1)|(a_1...a_(m-1)) for i=1, ..., m, where m|n indicates that m divides n. A Carmichael sequence has ...

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

A surface of revolution of the form r(phi)=a[1-esin^2phi-(3/8e^2+k)sin^2(2phi)], where k is a second-order correction to the figure of a rotating fluid.

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...

A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

A quintic curve is an algebraic curve of order five. Examples of quintic curves include the Burnside curve, butterfly catastrophe curve, and stirrup curve.