Iterated combinatorial density theorems

Iterated combinatorial density theorems

Matching Theorems for Combinatorial

Continuous Iterated Density Estimation

Geometric proofs for combinatorial theorems

There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3, 5-quadrangulation. The vertices of a 2, 4-hexangulation of the torus cannot be bicolored. Similar statements hold for 4, 8-triangulations and 2, 6-quadrangulations. We prove these results, of which the first two are known and the others seem t...

Matching Theorems for Combinatorial Geometries