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A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of ...

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

The phrase dependent percolation is used in two-dimensional discrete percolation to describe any general model in which the states of the various graph edges (in the case of ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...