Combinatorial decompositions of strict partitions and multi-sum Rogers-Ramanujan type identities

Abstract

While multi-sum Rogers-Ramanujan type identities have been extensively investigated through Bailey pairs, the constant term method, complex contour integration, and related techniques, many still lack an intrinsic combinatorial understanding. In this paper, we establish combinatorial interpretations for several families of triple-sum identities via structural decompositions of strict partitions. For one of these families, we extend the underlying combinatorial framework to obtain a general (m+1)-fold multi-sum identity. Leveraging these partition-theoretic interpretations, we construct explicit bijective proofs for all the corresponding identities. As an application, this constructive approach naturally yields some parameterized generalizations.

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BibTeX RIS

BibTeX

@misc{li2026combinatorial,
  title = {{Combinatorial decompositions of strict partitions and multi-sum Rogers-Ramanujan type identities}},
  author = {Haijun Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35234},
  eprint = {2610.35234},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35234},
}

RIS

TY  - UNPB
TI  - Combinatorial decompositions of strict partitions and multi-sum Rogers-Ramanujan type identities
AU  - Haijun Li
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35234
UR  - https://arxiv.org/abs/2610.35234
AB  - While multi-sum Rogers-Ramanujan type identities have been extensively investigated through Bailey pairs, the constant term method, complex contour integration, and related techniques, many still lack an intrinsic combinatorial understanding. In this paper, we establish combinatorial interpretations for several families of triple-sum identities via structural decompositions of strict partitions. For one of these families, we extend the underlying combinatorial framework to obtain a general (m+1)-fold multi-sum identity. Leveraging these partition-theoretic interpretations, we construct explicit bijective proofs for all the corresponding identities. As an application, this constructive approach naturally yields some parameterized generalizations.
ER  -

Abstract

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