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A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...

A sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Neil Sloane ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

The falling factorial (x)_n, sometimes also denoted x^(n__) (Graham et al. 1994, p. 48), is defined by (x)_n=x(x-1)...(x-(n-1)) (1) for n>=0. Is also known as the binomial ...

The rising factorial x^((n)), sometimes also denoted <x>_n (Comtet 1974, p. 6) or x^(n^_) (Graham et al. 1994, p. 48), is defined by x^((n))=x(x+1)...(x+n-1). (1) This ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...