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A pair of vertices (x,y) of a graph G is called an omega-critical pair if omega(G+xy)>omega(G), where G+xy denotes the graph obtained by adding the edge xy to G and omega(H) ...

Let S_n be the set of permutations of {1, 2, ..., n}, and let sigma_t be the continuous time random walk on S_n that results when randomly chosen transpositions are performed ...

One of the symbols { and } used in many different contexts in mathematics. Braces are used 1. To denote grouping of mathematical terms, usually as the outermost delimiter in ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

Let K be a number field, then each fractional ideal I of K belongs to an equivalence class [I] consisting of all fractional ideals J satisfying I=alphaJ for some nonzero ...

The clique covering number theta(G) of a graph G is the minimum number of cliques in G needed to cover the vertex set of G. Since theta(G) involves the minimum number of ...

The colon is the symbol ":". It is used in a number of different ways in mathematics. 1. To denote ratio or odds, as in 2:1 (voiced "two to one"). 2. To mean such that in ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...