Ali Kemal Uncu,
"Weighted Rogers--Ramanujan partitions and Dyson crank"
, in The Ramanujan Journal, 5-2017, ISSN: 1572-9303
Weighted Rogers--Ramanujan partitions and Dyson crank
Sprache des Titels:
In this paper, we refine a weighted partition identity of Alladi. We write formulas for generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results as well as the different statistics with the crank of a partition. In particular, we prove that the number of partitions into even number of distinct parts whose odd-indexed parts' sum is n is equal to the number of partitions of n with non-negative crank.