Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614160 | Journal of Mathematical Analysis and Applications | 2016 | 15 Pages |
Abstract
Cubic partitions are a special kind of bi-partitions whose name is inspired by a connection between a cubic continued fraction and an arithmetic property of this bi-partition. There are two partition statistics, namely rank and crank, for cubic partitions, which explain cubic partition congruences combinatorially. We obtain asymptotics for the number of cubic partitions of rank (resp. crank) m which reveal the distribution of the rank (resp. crank) among cubic partitions. As applications, we derive asymptotic inequalities between cubic partition rank and crank functions, and we remark upon the similarities and the differences between these and the corresponding inequalities for ordinary partitions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Byungchan Kim, Eunmi Kim, Hayan Nam,