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A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

A doubly nonnegative matrix is a real positive semidefinite n×n square matrix with nonnegative entries. Any doubly nonnegative matrix A of order n can be expressed as a Gram ...

If mu is a real measure (i.e., a measure that takes on real values), then one can decompose it according to where it is positive and negative. The positive variation is ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...