SIP classes and four-parameter partition identities
Abstract
The four-parameter weight of partitions played an important role in the theory of integer partitions, for its connection with various statistics, including the alternating sum and the BG-rank. In 2022, Andrews introduced the SIP classes, by which he reviewed a number of classic partition identities and provided new combinatorial insights. In this work, we extend the SIP classes and provide a unified method to study the four-parameter weight of partitions. By treating partitions with position parity as examples, we provide four-parameter partition identities related to these partition sets. And as corollary, we also present the generating functions that keep track of the BG-rank and the joint distribution of the number of odd parts and the alternating sum, respectively.
Keywords
Cite
@article{arxiv.2603.02575,
title = {SIP classes and four-parameter partition identities},
author = {Runqiao Li},
journal= {arXiv preprint arXiv:2603.02575},
year = {2026}
}