PreprintCC BY 4.0arXiv
Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts
Abstract
In recent work, authors defined b̅kr,s(n) to be the number of overcolored partition k-tuples wherein both even and odd parts are colored with r and s colors, respectively. This function generalizes the overcubic partition k-tuples studied by Chacon and Sellers. The present work gives a uniform framework for studying congruences for b̅kr,s(n) modulo odd primes. For example, we prove that, for n≥ 1, b̅4,24(5n)≡ 0pmod5.
Related
- Overcolored Partition k-tuples Restricted by Parity of the Parts
- On Certain Congruences for Partition k-Tuples with $5$-Cores
- Congruences for Overcubic Partition k-Tuples
- Nonexistence of Constant Congruences for the Cumulative Partition Function
- Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta-functions
BibTeX
@misc{thejitha2026congruences,
title = {{Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the Parts}},
author = {M. P. Thejitha and S. N. Fathima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32614},
eprint = {2609.32614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32614},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts
AU - M. P. Thejitha
AU - S. N. Fathima
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32614
UR - https://arxiv.org/abs/2609.32614
AB - In recent work, authors defined b̅^k_r,s(n) to be the number of overcolored partition k-tuples wherein both even and odd parts are colored with r and s colors, respectively. This function generalizes the overcubic partition k-tuples studied by Chacon and Sellers. The present work gives a uniform framework for studying congruences for b̅^k_r,s(n) modulo odd primes. For example, we prove that, for n≥ 1, b̅_4,2^4(5n)≡ 0pmod5.
ER -