The odd moments of ranks and cranks

• Main Authors: Chan, Song Heng, Kim, Byungchan, Andrews, George E.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics
• Online Access: https://hdl.handle.net/10356/98565; http://hdl.handle.net/10220/17801
• Institution: Nanyang Technological University

In this paper, we modify the standard definition of moments of ranks and cranks such that odd moments no longer trivially vanish. Denoting the new k-th rank (resp. crank) moments by (resp. ), we prove the following inequality between the first rank and crank moments.