Linked partition ideals, directed graphs and $q$-multi-summations

Combinatorics/Partitions Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, George Andrews, Ae Ja Yee, Matthew Katz.

Speaker: Shane Chern, Penn State University Math Dept

Abstract: Finding an Andrews-Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this talk, I will handle this problem in the setting of graph theory. With the generating function of directed graphs with an "empty" vertex, we then turn our attention to a $q$-difference system. This $q$-difference system eventually yields a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Finally, using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews-Gordon type generating function identities. These proofs also have an interesting connection with binary trees.

Room Reservation Information

Room Number: 106 McAllister

Date: 09/24/2019

Time: 11:15am - 12:05pm