Search Results for ""

A similarity transformation which preserves orientation, also called a homothety.

The 6-polyiamonds illustrated above.

The Diophantine equation x_1^2+x_2^2+...+x_n^2=ax_1x_2...x_n which has no integer solutions for a>n.

A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

Let sigma_infty(n) be the sum of the infinitary divisors of a number n. An infinitary k-multiperfect number is a number n such that sigma_infty(n)=kn. Cohen (1990) found 13 ...

The intersection number omega(G) of a given graph G is the minimum number of elements in a set S such that G is an intersection graph on S.

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.