On the asymptotic behavior of unimodal rank generating functions
  In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we extend Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions. 
Kathrin Bringmann and Byungchan Kim
math.NT math.CO