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Let v be a n-vector whose entries are each 1 (with probability p) or 0 (with probability q=1-p). An s-run is an isolated group of s consecutive 1s. Ignoring the boundaries, ...

A diamond-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0,y_0) that may affect the evolution of a two-dimensional cellular ...

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). In addition to the mathematical ...

The generalized Petersen graph GP(n,k), also denoted P(n,k) (Biggs 1993, p. 119; Pemmaraju and Skiena 2003, p. 215), for n>=3 and 1<=k<=|_(n-1)/2_| is a connected cubic graph ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

A Ruth-Aaron pair is a pair of consecutive numbers (n,n+1) such that the sums of the prime factors of n and n+1 are equal. They are so named because they were inspired by the ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

There are several definitions of "almost Hamiltonian" in use. As defined by Punnim et al. (2007), an almost Hamiltonian graph is a graph on n nodes having Hamiltonian number ...

Also called Chvátal's art gallery theorem. If the walls of an art gallery are made up of n straight line segments, then the entire gallery can always be supervised by |_n/3_| ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...