Variation on a theme of Nathan Fine. New weighted partition identities

JOURNAL OF NUMBER THEORY

卷:176

Article

Berkovich, Alexander¹  Uncu, Ali K.¹ 

[1] Univ Florida, Dept Math, 358 Little Hall, Gainesville, FL 32611 USA

关键词: Weighted count of partitions;    Gordon-Gollnitz partitions;    Rogers-Ramanujan partitions;    False theta functions;    Heine transformation;    q-Gauss summation;    Modular partitions;   

DOI  :  10.1016/j.jnt.2016.12.011

来源: Elsevier

【 摘 要 】

We utilize false theta function results of Nathan Fine to discover four new partition identities involving weights. These relations connect Gollnitz-Gordon type partitions and partitions with distinct odd parts, partitions into distinct parts and ordinary partitions, and partitions with distinct odd parts where the smallest positive integer that is not a part of the partition is odd and ordinary partitions subject to some initial conditions, respectively. Some of our weights involve new partition statistics, one is defined as the number of different odd parts of a partition larger than or equal to a given value and another one is defined as the number of different even parts larger than the first integer that is not a part of the partition. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free