Search Results for ""

The product of any number of perspectivities.

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

Dissect a triangle into smaller triangles, such that all have full edge contact with their neighbors. Label the corners 1, 2, and 3. Label all vertices with 1, 2, or 3, with ...

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

The abundance of a number n, sometimes also called the abundancy (a term which in this work, is reserved for a different but related quantity), is the quantity ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

An elliptic curve of the form y^2=x^3+n for n an integer. This equation has a finite number of solutions in integers for all nonzero n. If (x,y) is a solution, it therefore ...

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 ...