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Let C be an error-correcting code consisting of N codewords in which each codeword consists of n letters taken from an alphabet A of length q, and every two distinct ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

The probability that two elements P_1 and P_2 of a symmetric group generate the entire group tends to 3/4 as n->infty (Netto 1964, p. 90). The conjecture was proven by Dixon ...

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If xHx^(-1)=H for every element x in G, then ...

A set X is said to be nowhere dense if the interior of the set closure of X is the empty set. For example, the Cantor set is nowhere dense. There exist nowhere dense sets of ...

The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes. Because of the conflicting usage, it is probably best to avoid use of the ...

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

An ordered pair representation is a representation of a directed graph in which edges are specified as ordered pairs or vertex indices. The ordered pairs representation of a ...

An oriented knot is an oriented link of one component, or equivalently, it is a knot which has been given an orientation. Given an oriented knot K, reversing the orientation ...

Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...