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Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

Every finite group G of order greater than one possesses a finite series of subgroups, called a composition series, such that I<|H_s<|...<|H_2<|H_1<|G, where H_(i+1) is a ...

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

In voting theory, a Condorcet candidate is a candidate who always wins in a 2-person election but loses in larger election. For example, consider the 6-tuples of 6-sided die ...

The Conway polynomial del _L(x), sometimes known as the Conway-Alexander polynomial, is a modified version of the Alexander polynomial Delta_L(x) that was formulated by J. H. ...

The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...