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A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

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 ...

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

The elliptic curve factorization method, abbreviated ECM and sometimes also called the Lenstra elliptic curve method, is a factorization algorithm that computes a large ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...