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An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...

A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.

The usual type of vector, which can be viewed as a contravariant tensor ("ket") of tensor rank 1. Contravariant vectors are dual to one-forms ("bras," a.k.a. covariant ...

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

A sphere with four punctures occurring where a knot passes through the surface.

Consider a set of points X_i on an attractor, then the correlation integral is C(l)=lim_(N->infty)1/(N^2)f, where f is the number of pairs (i,j) whose distance |X_i-X_j|<l. ...

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

A covariant tensor of rank 1, more commonly called a one-form (or "bra").

An n×n square matrix M with M_(ii) = 1 (1) M_(ij) = M_(ji)>1 (2) for all i,j=1, ..., n.