Constructions of Macaulay Posets and Macaulay Rings
Combinatorics
2026-04-14 v2 Commutative Algebra
Abstract
A poset is Macaulay if its partial order and an additional total order interact well. Analogously, a ring is Macaulay if the partial order defined on its monomials by division interacts nicely with any total monomial order. We investigate methods of obtaining new structures through combining Macaulay rings and posets by means of certain operations inspired by topology. We examine whether these new structures retain the Macaulay property, identifying new classes of posets and rings for which the operations preserve the Macaulay property.
Keywords
Cite
@article{arxiv.2502.15166,
title = {Constructions of Macaulay Posets and Macaulay Rings},
author = {Penelope Beall and Erenay Boyali and Nancy Chen and Ellen Chlachidze and Trong Toan Dao and Frederic Garvey and Mitchell Johnson and Yu Olivier Li and Nikola Kuzmanovski and Kelvin Ma and Treanungkur Mal and Rukshan Marasinghe Mudiyanselage and Quinlan Mayo and Nava Minsky-Primus and Alexandra Seceleanu and Sriram Veerapaneni},
journal= {arXiv preprint arXiv:2502.15166},
year = {2026}
}
Comments
Final version to appear in the Electronic Journal of Combinatorics