Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated just now
PreprintCC BY 4.0arXiv

Overcolored Partition k-tuples Restricted by Parity of the Parts

  • M. P. Thejitha
  • S. N. Fathima
Open at sourcePDFDOICite

Abstract

In this paper, we study the combinatorial object b̅kr,s(n) which counts the overcolored partition k-tuples wherein both even and odd parts are colored with r and s colors, respectively. We extend results of Chacon and Sellers for several families of r,s and k. We also establish divisibility properties for b̅kr,s(n) modulo prime p and conclude with new congruences modulo powers of $2$. The techniques involved to obtain our results rely on theta function identities and modular forms.

Related

  1. Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts
    M. P. Thejitha, S. N. Fathima
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. On Certain Congruences for Partition k-Tuples with $5$-Cores
    Saikat Maity
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Congruences for Overcubic Partition k-Tuples
    Daniel Chacón, James A. Sellers
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. A perimeter analogue of Franklin's identity and an inequality related to the parity of parts
    Philip Cuthbertson
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Untrodden pathways in the study of partitions with parts separated by parity
    Nargish Punia, Rahul Kumar
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{thejitha2026overcolored,
  title = {{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.2609.03926},
  eprint = {2609.03926},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03926},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Overcolored Partition k-tuples Restricted by Parity of the Parts
AU  - M. P. Thejitha
AU  - S. N. Fathima
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.03926
UR  - https://arxiv.org/abs/2609.03926
AB  - In this paper, we study the combinatorial object b̅^k_r,s(n) which counts the overcolored partition k-tuples wherein both even and odd parts are colored with r and s colors, respectively. We extend results of Chacon and Sellers for several families of r,s and k. We also establish divisibility properties for b̅^k_r,s(n) modulo prime p and conclude with new congruences modulo powers of $2$. The techniques involved to obtain our results rely on theta function identities and modular forms.
ER  -