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Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

A modified spherical Bessel function of the first kind (Abramowitz and Stegun 1972), also called a "spherical modified Bessel function of the first kind" (Arfken 1985), is ...

By asking a small number of innocent-sounding questions about an unknown number, it is possible to reconstruct the number with absolute certainty (assuming that the questions ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. ...

The uniformity conjecture postulates a relationship between the syntactic length of expressions built up from the natural numbers using field operations, exponentials, and ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

A symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...