Weighted Rogers–Ramanujan partitions and Dyson crank

被引：0
作者：
Ali Kemal Uncu
机构：
[1] University of Florida,Department of Mathematics
来源：
The Ramanujan Journal | 2018年 / 46卷
关键词：
Dyson crank; Partitions; Rogers–Ramanujan; Weighted partition identities; 05A15; 05A17; 05A19; 11B75; 11P81; 11P84;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：579 / 591
页数：12
相关论文
共 11 条
  • [1] Alladi K(1997)Partition identities involving gaps and weights Trans. Am. Math. Soc. 349 5001-5019
  • [2] Alladi K(2002)New weighted Rogers–Ramanujan partition theorems and their implications Trans. Am. Math. Soc. 354 2557-2577
  • [3] Berkovich A(1988)Dyson’s Crank of a Partition Bull. Am. Math. Soc. (N.S.) 18 167-171
  • [4] Andrews GE(1951)On some new types of partitions associated with generalized Ferrers graphs Proc. Camb. Philos. 47 679-686
  • [5] Garvan FG(2002)Some observations on Dysons new symmetries of partitions J. Comb. Theory A 100 61-93
  • [6] Auluck FC(2006)A four-parameter partition identity Ramanujan J. 12 315-320
  • [7] Berkovich A(2009)The Andrews–Stanley partition function and Al-Salam–Chihara polynomials Discrete Math. 309 151-175
  • [8] Garvan FG(undefined)undefined undefined undefined undefined-undefined
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