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Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/22944
Title: 
Weighted generalized crank moments for k-colored partitions and Andrews-Beck type congruences
Authors: 
Lin, Bernard L. S.
Peng, Lin
Toh, Pee Choon
Subjects: 
Rank and crank moments
k-colored partitions
Andrews-Beck type congruences
Partition statistics
Issue Date: 
2021
Citation: 
Lin, B. L. S., Peng, L., & Toh, P. C. (2021). Weighted generalized crank moments for k-colored partitions and Andrews-Beck type congruences. Discrete Mathematics, 344(8), Article 112450. https://doi.org/10.1016/j.disc.2021.112450
Abstract: 
Recently, Beck studied a new partition statistic which involves counting the total number of parts of a partition with certain rank or crank. Andrews proved two of Beck's conjectures related to ranks. Chern subsequently proved several results involving weighted rank and crank moments and deduced a number of similar Andrews-Beck type congruences. In this paper, we show that some of Chern's results can be explained by a simple combinatorial argument, and extend this approach to the study of k-colored partitions. As a consequence, we derive a large number of new Andrews-Beck type congruences for k-colored partitions.
Description: 
This is the final draft, after peer-review, of a manuscript published in Discrete Mathematics. The published version is available online at https://doi.org/10.1016/j.disc.2021.112450
URI: 
http://hdl.handle.net/10497/22944
ISSN: 
0012-365X
DOI: 
10.1016/j.disc.2021.112450
Grant ID: 
National Natural Science Foundation of China (Grant no.: 11871246)
Natural Science Foundation of Fujian Province of China (Grant no.: 2019J01328)
Program for New Century Excellent Talents in Fujian Province University (Grant no.: B17160)
Funding Agency: 
National Natural Science Foundation of China
Natural Science Foundation of Fujian Province of China
Fujian Province University, China
File Permission: 
Embargo_20230901
File Availability: 
With file
Appears in Collections:Journal Articles

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