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PreprintCC BY 4.0arXiv

Congruences for the Andrews--Uncu partition function β„°π’ͺu(n)

  • Nayandeep Deka Baruah
  • Hirakjyoti Das
  • Manjil P. Saikia
  • Abhishek Sarma
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Abstract

In 2018, Andrews defined and studied the partition function β„°π’ͺ(n), which counts the number of partitions of n where each even part is less than each odd part. Thereafter, Uncu considered a different subset of such partitions, namely those partitions counted by β„°π’ͺ(n) where there are no repeated even parts (we denote the number of such partitions by β„°π’ͺu(n)). In this paper, we prove several congruences modulo powers of $2$ for β„°π’ͺu(n). We also prove some infinite families of congruences as well as a recurrence for the number of this class of partitions. Our methods involve elementary, algorithmic, and modular form techniques.

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Cite

BibTeXRIS
BibTeX
@misc{baruah2026congruences,
  title = {{Congruences for the Andrews--Uncu partition function $\mathcalEO_u(n)$}},
  author = {Nayandeep Deka Baruah and Hirakjyoti Das and Manjil P. Saikia and Abhishek Sarma},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37920},
  eprint = {2609.37920},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37920},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Congruences for the Andrews--Uncu partition function β„°π’ͺ_u(n)
AU  - Nayandeep Deka Baruah
AU  - Hirakjyoti Das
AU  - Manjil P. Saikia
AU  - Abhishek Sarma
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37920
UR  - https://arxiv.org/abs/2609.37920
AB  - In 2018, Andrews defined and studied the partition function β„°π’ͺ(n), which counts the number of partitions of n where each even part is less than each odd part. Thereafter, Uncu considered a different subset of such partitions, namely those partitions counted by β„°π’ͺ(n) where there are no repeated even parts (we denote the number of such partitions by β„°π’ͺ_u(n)). In this paper, we prove several congruences modulo powers of $2$ for β„°π’ͺ_u(n). We also prove some infinite families of congruences as well as a recurrence for the number of this class of partitions. Our methods involve elementary, algorithmic, and modular form techniques.
ER  -