Realizable Posets Of Some Monomial Ideals

Joseph Clark - Winner of the Judge’s Choice Award

A support poset is a useful algebraic tool for depolarizing monomial ideals to study the reliability of multistate coherent systems (Mohammadi et al., 2020). The support poset encodes the relationship between the variable of some polynomial ring and the minimal monomial generators of the ideal. It is known that a given poset may be the support poset of many square-free monomial ideals, while other posets are not realizable as support posets. However, a current classification does not exist for all posets. In this talk, we will discuss specific classes of posets that are realizable as support posets as well as classes of posets that are not realizable as support posets.

• Joseph Clark graduated from Fort Mill High School in Fort Mill, SC, in 2014 before joining the United States Marine Corps and serving for five years. Joseph is a double major in Mathematics and Computer Information Systems. His achievements include serving as a teaching assistant for Math 121, working as a peer tutor, and presenting undergraduate research in mathematics and computer information systems at multiple locations during his time at Lander.