Coarsests Subdivisions of Hypersimplices

This repository contains the data and code necessary to reproduce the results of [1].

Data

	Delta(2,7)	Delta(3,6)
mptopcom input and output	link	link
Classes of rays of the secondary fan	link	link

Code

The triangulations are produced by mptopcom [3] and then processed by polymake [2] scripts.

rays_of_sec_cones.pl

This script gets as input an input and an output file of mptopcom. The input file is necessary to ensure that the script works with the same group and point configuration as mptopcom. The output is a polymake data file containing a set of vectors. These vectors are the rays of the secondary cones of the triangulations in the mptopcom output. Since the group acts on the triangulations and thereby on the rays, there is only one representative per ray orbit.

process_rays.pl

For large output of mptopcom it makes sense to split it into chunks and run rays_of_sec_cones.pl separately on every chunk. This script unifies the intermediate results and does additional postprocessing:

• It associates an ID to every ray representative.
• It produces a histogram of how many rays exhibit a given spread.

References

[1] Laura Casabella, Michael Joswig, Lars Kastner: Coarsest Subdivisions of Hypersimplices. arxiv.

[2] polymake - open source software for research in polyhedral geometry.

[3] mptopcom - computing triangulations of point configurations in parallel.