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PreprintCC BY-NC-ND 4.0arXiv

Part Size Count in Cylindric Partitions and Bijections for Small Profiles

  • Kağan Kurşungöz
  • Halime Ömrüuzun Seyrek
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Abstract

We first study the part size statistic in cylindric partitions, listing some specializations of a crude but general formula. Then, we establish bijections between ordinary partitions and cylindric partitions of small profiles with additional restrictions. Lastly, we extend earlier formulas for generating functions of cylindric partitions into distinct parts and functional equations of unrestricted cylindric partition generating functions, involving the part size statistic.

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Cite

BibTeXRIS
BibTeX
@misc{kursungoz2026part,
  title = {{Part Size Count in Cylindric Partitions and Bijections for Small Profiles}},
  author = {Kağan Kurşungöz and Halime Ömrüuzun Seyrek},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36910},
  eprint = {2609.36910},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36910},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Part Size Count in Cylindric Partitions and Bijections for Small Profiles
AU  - Kağan Kurşungöz
AU  - Halime Ömrüuzun Seyrek
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36910
UR  - https://arxiv.org/abs/2609.36910
AB  - We first study the part size statistic in cylindric partitions, listing some specializations of a crude but general formula. Then, we establish bijections between ordinary partitions and cylindric partitions of small profiles with additional restrictions. Lastly, we extend earlier formulas for generating functions of cylindric partitions into distinct parts and functional equations of unrestricted cylindric partition generating functions, involving the part size statistic.
ER  -