6 papers · 1 filter
Simplicial cell decompositions of
Basudeb Datta, Jonathan Spreer
According to a well-known result in geometric topology, we have \linebreak , where $\operatorname{Sym}(…
Sampling triangulations of manifolds using Monte Carlo methods
Eduardo G. Altmann, Jonathan Spreer
We propose a Monte Carlo method to efficiently find, count, and sample abstract triangulations of a given manifold M. The method is based on a biased random walk through all possib…
Hopf triangulations of spheres and equilibrium triangulations of projective spaces
Wolfgang Kühnel, Jonathan Spreer
Following work by the first author and Banchoff, we investigate triangulations of real and complex projective spaces of real and complex dimension that are adapted to the decom…
A Uniform Sampling Procedure for Abstract Triangulations of Surfaces
Rajan Shankar, Jonathan Spreer
We present a procedure to sample uniformly from the set of combinatorial isomorphism types of balanced triangulations of surfaces - also known as graph-encoded surfaces. For a give…
Average Betti numbers of induced subcomplexes in triangulations of manifolds
Giulia Codenotti, Francisco Santos, Jonathan Spreer
We study a variation of Bagchi and Datta's -vector of a simplicial complex , whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of . W…
Short proof of two cases of Chvátal's conjecture
Jorge Olarte, Francisco Santos, Jonathan Spreer
In 1974 Chvátal conjectured that no intersecting family in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture…