Transfinite mutations in the completed infinity-gon

Transfinite Equations in Transfinite Strings

Inscribing a regularm-gon in a regular n-gon

We find necessary and sufficient conditions on m and n for inscribing a regular m-gon in a regular n-gon. Mathematics Subject Classification (2010). Primary 51M20; Secondary 52C15.

On a Cluster Category of Infinite Dynkin Type, and the Relation to Triangulations of the Infinity-gon

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D(s,Σs) is k for i = 0 and i = 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using (de)suspensions, direct sums, direct summands, ...

Longest Hamiltonian in Nodd-Gon

We single out the polygonal paths of order that solve each of the 1 odd n  2 odd n       different longest non-cyclic Euclidean Hamiltonian path problems in      iπ e 1 , odd n n n ij n n K d     networks by an arithmetic algorithm. As by product, the procedure determines the winding index of cyclic Hamiltonian polygonals on the vertices of a regular polygon.

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...