Search Results for ""

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

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 ...

The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

Any four mutually tangent spheres determine six points of tangency. A pair of tangencies (t_i,t_j) is said to be opposite if the two spheres determining t_i are distinct from ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

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 alternating factorial is defined as the sum of consecutive factorials with alternating signs, a(n)=sum_(k=1)^n(-1)^(n-k)k!. (1) They can be given in closed form as ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...