8
votes
1answer
299 views

Question about tetrahedron decomposition

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrahedron for which this ...
4
votes
0answers
105 views

What is known about the number of permissible simplicial complexes given the number of k-cells?

Motivation: I am working on a problem that reduces to finding simplicial complexes given some data (details are unnecessary), but all I have managed to wrangle from my input is the number of cells of ...
5
votes
2answers
467 views

Generalization of Hamiltonian cycles to “Hamiltonian spheres”

One possible generalization of a Hamiltonian cycle in a triangulated plane graph is what could be called a Hamiltonian sphere: a collection of triangles within a simplicial complex in $\mathbb{R}^3$ ...
6
votes
2answers
278 views

Simplicial and cubical decompositions of low valence

Every surface can be triangulated in such a way that at most 7 trianlges meet at one vertex. Every surface can be decomposed in squares such that at every vertex at most 5 suqares meet. For surfaces ...
2
votes
3answers
872 views

Boolean network as a gauge field

Consider a set of N binary-state nodes at "time" t, each of which is a (boolean) transition function of two nodes in the set, evaluated at time t-1. Thus there are N of these boolean functions of two ...