The k-fractal of a simplicial complex

The k-fractal of a simplicial complex

The k-polynomial of a simplicial complex C is the function kC(x)= ∑ i¿1 fix i where fi is the number of i-faces in C. These k-polynomials are closed under composition, and we are lead to ask: for higher composites of a complex C with itself, what happens to the roots of their k-polynomials? We prove that they converge to the Julia set of kC(x), thereby associating with C a fractal. For 2-dimens...

Invariance of the barycentric subdivision of a simplicial complex

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Fitting a Simplicial Complex using a Variation of k-means

In this paper we give a simple two stage algorithm for approximating a point cloud S ⊂ Rm by a simplicial complex K. The first stage is an iterative fitting procedure that generalizes k-means clustering, while the second stage involves deleting redundant simplices. A form of dimension reduction of S is obtained as a consequence.

invariance of the barycentric subdivision of a simplicial complex

‎in this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎we also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Simplicial Approach to Fractal Structures