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A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

Let a closed interval [a,b] be partitioned by points a<x_1<x_2<...<x_(n-1)<b, where the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ...

Calculus I

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the partition. The spelling "Ferrars" (Skiena ...

In complex analysis, a branch (also called a sheet) is a portion of the range of a multivalued function over which the function is single-valued. Combining all the sheets ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...

A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...