Abstracts
for the Seminar

Fall 2024

**Speaker: **Nik Kuzmanovski, University of Notre Dame

**Title: **Macaulay posets and rings

**Time:** 2:30 PM, Monday, October 28, 2024

**Place:** Malott 206

**Abstract:** Macaulay proved that for every homogeneous ideal, there exists a lex ideal with the same Hilbert function. This theorem is often stated in terms of $O$-sequences or an inequality involving binomial coefficients. One of the key techniques to proving Macaulay's theorem is a combinatorial inequality that provides a lower bound on the growth of shadows in the infinite grid $N^d$. This result has had an enormous influence on algebra and combinatorics over the past century. Generalizations of Macaulay's Theorem will be presented.

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