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Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts

  • Manjil P. Saikia
  • Prabal Talukdar
  • Dazhao Tang
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Abstract

Let po̅k(n) denote the number of k-colored overpartitions of n into odd parts. For every odd number of colors, we establish infinite families of internal congruences modulo high powers of $2$. The proof proceeds by expressing the relevant difference generating functions as a fixed theta quotient multiplied by polynomials in an auxiliary function. Uniform lower bounds for the $2$-adic valuations of the polynomial coefficients then yield the stated internal congruences. These results generalize an internal congruence of Saikia, Sarma and Sellers (J. Ramanujan Math. Soc.~2025) on overpartition triples into odd parts.

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Cite

BibTeXRIS
BibTeX
@misc{saikia2026internal,
  title = {{Internal congruences modulo powers of 2 for $k$-colored overpartitions into odd parts}},
  author = {Manjil P. Saikia and Prabal Talukdar and Dazhao Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.11806},
  eprint = {2609.11806},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11806},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts
AU  - Manjil P. Saikia
AU  - Prabal Talukdar
AU  - Dazhao Tang
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.11806
UR  - https://arxiv.org/abs/2609.11806
AB  - Let po̅_k(n) denote the number of k-colored overpartitions of n into odd parts. For every odd number of colors, we establish infinite families of internal congruences modulo high powers of $2$. The proof proceeds by expressing the relevant difference generating functions as a fixed theta quotient multiplied by polynomials in an auxiliary function. Uniform lower bounds for the $2$-adic valuations of the polynomial coefficients then yield the stated internal congruences. These results generalize an internal congruence of Saikia, Sarma and Sellers (J. Ramanujan Math. Soc.~2025) on overpartition triples into odd parts.
ER  -