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Let v be a n-vector whose entries are each 1 (with probability p) or 0 (with probability q=1-p). An s-run is an isolated group of s consecutive 1s. Ignoring the boundaries, ...

An infinite set, such as the real numbers, which is not countably infinite.

A distance graph with distance set (0,1].

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

A mathematical object (such as a set or function) is said to bounded if it possesses a bound, i.e., a value which all members of the set, functions, etc., are less than.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

The usual number of scalar operations (i.e., the total number of additions and multiplications) required to perform n×n matrix multiplication is M(n)=2n^3-n^2 (1) (i.e., n^3 ...