University of Minnesota Combinatorics Seminar: 2020-2021

Date: 11/13/2020

Speaker: Justin Chen

Free Resolutions of Function Classes Via Order Complexes
Function classes are collections of Boolean functions on a finite set. In 2017, a method of studying function classes via commutative algebra, by associating a squarefree monomial ideal to a function class, was introduced by Yang. I will describe this connection, as well as some free resolutions and Betti numbers for these ideals for an interesting collection of function classes, corresponding to intersection-closed posets. This is joint work with Chris Eur, Greg Yang, and Mengyuan Zhang.

Free Resolutions of Function Classes Via Order Complexes

Function classes are collections of Boolean functions on a finite set. In 2017, a method of studying function classes via commutative algebra, by associating a squarefree monomial ideal to a function class, was introduced by Yang. I will describe this connection, as well as some free resolutions and Betti numbers for these ideals for an interesting collection of function classes, corresponding to intersection-closed posets. This is joint work with Chris Eur, Greg Yang, and Mengyuan Zhang.