{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-weak-lefschetz-property-and-unimodality","title":"The Weak Lefschetz property and unimodality of Hilbert functions of random monomial algebras","arxiv_id":"2402.17618","date":"2024-02-27","proceeding":null,"authors":["Uwe Nagel","Sonja Petrović"],"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.","url_abs":"https://arxiv.org/abs/2402.17618v1","url_pdf":"https://arxiv.org/pdf/2402.17618v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-weak-lefschetz-property-and-unimodality","repo_url":"https://github.com/sondzus/rmi-hilbert-wlp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}