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Let a group G have a group presentation G=<x_1,...,x_n|r_j(x_1,...,x_n),j in J> so that G=F/R, where F is the free group with basis {x_1,...,x_n} and R is the normal subgroup ...

In continuum percolation theory, the Boolean-Poisson model is a Boolean model driven by a stationary point process X which is a Poisson process. The Boolean-Poisson model is ...

A Calkin-Wilf tree is a special type of binary tree obtained by starting with the fraction 1/1 and iteratively adding a/(a+b) and (a+b)/b below each fraction a/b. The ...

The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

A d-dimensional discrete percolation model on a regular point lattice L=L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...