Adam Van Tuyl Department of Mathematics and Statistics McMaster University Hamilton, ON, Canada L8S 4L8 vantuyl@math.mcmaster.ca

Programs for Levelable Simplicial Complexes

In my paper

• Simplicial complexes and Macaulay's inverse systems (with F. Zanello)
  Mathematische Zeitschrift 265 (2010) 151-160.

we introduced the notion of a levelable simplicial complex. Roughly speaking, a simplicial complex is levelable if the Stanley-Reisner ring of the associated simplicial complex can be turned into a level artinian algebra by adding the appropriate powers of the variables to the ideal.

One of the main results of this paper (Theorem 4.1) is to show that a simplicial complex is levelable if and only if there is integral solution to a system of linear equations formed from the facet set of the simplicial complex.

As promised in the paper (Remark 4.2), we have included a program written for Mathematica, to check if a simplicial complex is levelable.

You can download the scripts here:

• Mathematica program for determining if a simplicial complex is levelable.

This program was written by Matt Miller and Alex Schaefer both graduate students at Michigan Tech University. We thank them for their help.