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A pair of elements (p_i,p_j) is called an inversion in a permutation p if i>j and p_i<p_j (Skiena 1990, p. 27; Pemmaraju and Skiena 2003, p. 69). For example, in the ...

A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The ...

A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted trees of n nodes is T_(n-1), where T_(n-1) is the number of rooted trees of n-1 ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

A number s of trials in which the probability of success p_i varies from trial to trial. Let x be the number of successes, then var(x)=spq-ssigma_p^2, (1) where sigma_p^2 is ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

The word population has a number of distinct but closely related meanings in statistics. 1. A finite and actually existing group of objects which, although possibly large, ...

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...