Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 4, 2016 - 16:00 to 16:45

Location:

BAT 250

Local Speaker:

Abstract:

We discuss a specific use of Bailey's Lemma to arrive at inequalities between the moments of partition rank and crank functions. We first review Garvan's work on the rank and crank of partitions and the authors work on the rank and crank of overpartitions. We use this to motivate the statement of our main theorem which, when given a suitable Bailey pair, yields a rank-like function and crank-like; an identity for the difference of the symmetrized moments; an inequality between the symmetrized moments; an inequality between the ordinary moments; and a non-negative weighted count on certain vector partitions. This work is the end result of one project from this summer's REU program at OSU, and is joint work with Catherine Babecki and Geoffrey Sangston.