The Weak Lefschetz property and unimodality of Hilbert functions of random monomial algebras
Abstract
In this work, we investigate the presence of the weak Lefschetz property (WLP) and Hilbert functions for various types of random standard graded Artinian algebras. If an algebra has the WLP then its Hilbert function is unimodal. Using probabilistic models for random monomial algebras, our results and simulations suggest that in each considered regime the Hilbert functions of the produced algebras are unimodal with high probability. The WLP appears to be present with high probability most of the time. However, we propose that there is one scenario where the generated algebras fail to have the WLP with high probability.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.17618
 arXiv:
 arXiv:2402.17618
 Bibcode:
 2024arXiv240217618N
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Probability
 EPrint:
 Supplementary Macaulay2 code for generating random monomial algebras is provided through a github link