PreprintarXiv licencearXiv
On Certain Congruences for Partition k-Tuples with $5$-Cores
Abstract
Let At,k(n) denote the number of partition k-tuples of n with t-cores. Using fifth-order modular equations and the Atkin U5-operator, we prove the congruences A5,125i+21(25n+r)≡ 0 pmod53 for r∈{9,14,19,24}, A5,125i+41(25n+r)≡ 0 pmod53 for r∈{19,24}, and A5,125i+111(125n+r)≡ 0 pmod54 for r∈{39,64,89,114}, which were stated by Tang \cite{tang2025iterative}.
Related
- Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts
- Congruences for Overcubic Partition k-Tuples
- Partitions with designated summands: k-tuples and their congruences
- Overcolored Partition k-tuples Restricted by Parity of the Parts
- Nonexistence of Constant Congruences for the Cumulative Partition Function
BibTeX
@misc{maity2026certain,
title = {{On Certain Congruences for Partition $k$-Tuples with $5$-Cores}},
author = {Saikat Maity},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00693},
eprint = {2611.00693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00693},
}
RIS
TY - UNPB
TI - On Certain Congruences for Partition k-Tuples with $5$-Cores
AU - Saikat Maity
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00693
UR - https://arxiv.org/abs/2611.00693
AB - Let A_t,k(n) denote the number of partition k-tuples of n with t-cores. Using fifth-order modular equations and the Atkin U_5-operator, we prove the congruences A_5,125i+21(25n+r)≡ 0 pmod5^3 for r∈{9,14,19,24}, A_5,125i+41(25n+r)≡ 0 pmod5^3 for r∈{19,24}, and A_5,125i+111(125n+r)≡ 0 pmod5^4 for r∈{39,64,89,114}, which were stated by Tang \cite{tang2025iterative}.
ER -