author = {Uncu Ali Kemal},
title = {{Weighted Rogers--Ramanujan partitions and Dyson crank}},
language = {english},
abstract = {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.},
journal = {The Ramanujan Journal},
pages = {--},
isbn_issn = { ISSN 1572-9303},
year = {2017},
month = {May},
refereed = {yes},
length = {0},
url = {https://doi.org/10.1007/s11139-017-9903-8}