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arXiv:1705.10067 [math.CO]AbstractReferencesReviewsResources

On a generalized crank for $k$-colored partitions

Shishuo Fu, Dazhao Tang

Published 2017-05-29Version 1

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.

Comments: 12 pages,1 table
Categories: math.CO
Subjects: 11P81, 11P83, 05A17, 05A20
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