Programs based Simplicial Complexes and Macaulay's Inverse Systems by Van Tuyl and Zanello<

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

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:

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

Last Updated: Dec. 4, 2007
URL: http://ms.mcmaster.ca/~vantuyl/research/Levelable_VanTuyl_Zanello.html