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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