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The number of nondecreasing lists {a_1,a_2,...,a_n} consisting of n elements 1<=a_i<=k is given by the binomial coefficient N(n,k)=(n+k-1; n-1). For example, there are six ...

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

The number of "arrangements" in an ordering of n items is given by either a combination (order is ignored) or a permutation (order is significant). An ordering (or order) is ...

The four of Hilbert's axioms which concern the arrangement of points.

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

The y- (vertical) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...

A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former ...

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.