Sequences of odd length in strict partitions IV: the combinatorics of parameterized Rogers-Ramanujan type identities

2025/09/29 by Li, Haijun
#05A17 #05A19 #11P84 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.24942

Abstract

In the first three papers, we conducted a series of discussions on the statistics of strict partitions and Rogers-Ramanujan partitions, specifically the sequences of odd length (denoted as sol) and its extensions. We established bijections for some Rogers-Ramanujan type identities. This paper will continue that series of work, and first we will use the bijective method to re-establish several parameterized Rogers-Ramanujan type identities, which appeared in the recent work of Hao-Kuai-Xia and Li-Wang. Moreover, we focus on the work of Chen-Yin and parameterize their main results, where the sol has evolved.

Citations

• Rogers--Ramanujan Type Identities for Rank Two Partial Nahm Sums
• Sequences of odd length in strict partitions II: the 2-measure and refinements of Euler's theorem
• Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities
• Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index (1,2,2)
• Rogers-Ramanujan type identities involving double, triple and quadruple sums
• Multidimensional Rogers-Ramanujan type identities with parameters

Related

• Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities
• Partition identities associated to Rogers-Ramanujan type identities
• One-Parameter Generalizations of Rogers-Ramanujan Type Identities
• IdentityFinder and some new identities of Rogers-Ramanujan type
• Refinements of the Rogers-Ramanujan identities