Wonwoo Kang (강원우), June 9, Tuesday, 6-7 PM, Unimodality and Cluster Algebras
Keimyung Discrete Math Seminar (계명 이산수학 세미나)
Date and Time: June 9, Tuesday, 6-7 PM
Title : Unimodality and Cluster Algebras
Speaker: Wonwoo Kang (강원우), International Center for Mathematical Sciences - Sofia (ICMS-Sofia)
Location: Room 324
Abstract: We prove that the rank polynomial of the lattice of order ideals of a loop fence poset is unimodal. This structure arises as the poset of join-irreducibles in the lattice of good matchings of loop graphs associated with notched arcs. Such polynomials can be obtained by evaluating all coefficient variables of an $F$-polynomial at a single variable $q$. We also establish that the rank polynomial of any tagged arc, whether plain or notched, is unimodal and satisfies a symmetry condition known as almost interlacing. We conclude by conjecturing that products of these polynomials are also unimodal. This is joint work with Kyeongjun Lee and Eunsung Lim.