Constructions of Macaulay Posets and Macaulay Rings
Penelope Beall, Erenay Boyali, Nancy Chen, Ellen Chlachidze, Trong Toan Dao, Frederic Garvey, Mitchell Johnson, Yu Olivier Li, Nikola Kuzmanovski, Kelvin Ma, Treanungkur Mal, Rukshan Marasinghe Mudiyanselage, Quinlan Mayo, Nava Minsky-Primus, Alexandra Seceleanu, Sriram Veerapaneni
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.