On a generalized crank for k-colored partitions

2017/05/29 by Fu, Shishuo, Tang, Dazhao
#05A17 #05A20 #11P81 #11P83 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.10067

Abstract

A generalized crank (k-crank) for k-colored partitions is introduced. Following the work of Andrews-Lewis and Ji-Zhao, we derive two results for this newly defined k-crank. Namely, we first obtain some inequalities between the k-crank counts M_k(r,m,n) for m=2,3 and 4, then we prove the positivity of symmetrized even k-crank moments weighted by the parity for k=2 and 3. We conclude with several remarks on furthering the study initiated here.

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