Weighted generalized crank moments for k-colored partitions and Andrews-Beck type congruences

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. (C) 2021 Elsevier B.V. All rights reserved.