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Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

When a Young tableau is constructed using the so-called insertion algorithm, an element starts in some position on the first row, from which it may later be bumped. In ...

The Paley class of a positive integer m=0 (mod 4) is defined as the set of all possible quadruples (k,e,q,n) where m=2^e(q^n+1), (1) q is an odd prime, and k={0 if q=0; 1 if ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

A theory which satisfies all the Eilenberg-Steenrod axioms with the possible exception of the long exact sequence of a pair axiom, as well as a certain additional continuity ...

The quadratic class number constant is a constant related to the average behavior of class numbers of real quadratic fields. It is given by Q = product_(p)[1-1/(p^2(p+1))] ...