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Let G be a simple graph with nonsingular (0,1) adjacency matrix A. If all the diagonal entries of the matrix inverse A^(-1) are zero and all the off-diagonal entries of ...

Given a sample of n variates X_1, ..., X_N, reorder them so that Y_1<Y_2<...<Y_N. Then Y_i is called the ith order statistic (Hogg and Craig 1970, p. 146), sometimes also ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

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, ...

If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

The sequence {|_(3/2)^n_|} is given by 1, 1, 2, 3, 5, 7, 11, 17, 25, 38, ... (OEIS A002379). The first few composite |_(3/2)^n_| occur for n=8, 9, 10, 11, 12, 13, 14, 15, 16, ...

A primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...