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PreprintCC BY 4.0arXiv

Colored Partitions and Minimal Excludants

  • Suverchla Arora
  • Meenakshi Rana
  • Shruti Sharma
  • Nilanjan Bag
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Abstract

In this article, we introduce the concept of minimal excludants in colored partitions and extend it to the framework of least r-gaps. In particular, we focus on k-colored partitions and cubic partitions, deriving the generating functions for the sums of minimal excludants and least r-gaps, and analyzing their asymptotic behaviors. Notably, the presented theory is comprehensively extended by the systematic generalization of each result for minimal excludants in k-colored partitions to the case of least r-gaps. We introduce generalized cubic partitions and discover the minimal excludant, as well as several additional results.

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Cite

BibTeXRIS
BibTeX
@misc{arora2026colored,
  title = {{Colored Partitions and Minimal Excludants}},
  author = {Suverchla Arora and Meenakshi Rana and Shruti Sharma and Nilanjan Bag},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34155},
  eprint = {2610.34155},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34155},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Colored Partitions and Minimal Excludants
AU  - Suverchla Arora
AU  - Meenakshi Rana
AU  - Shruti Sharma
AU  - Nilanjan Bag
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34155
UR  - https://arxiv.org/abs/2610.34155
AB  - In this article, we introduce the concept of minimal excludants in colored partitions and extend it to the framework of least r-gaps. In particular, we focus on k-colored partitions and cubic partitions, deriving the generating functions for the sums of minimal excludants and least r-gaps, and analyzing their asymptotic behaviors. Notably, the presented theory is comprehensively extended by the systematic generalization of each result for minimal excludants in k-colored partitions to the case of least r-gaps. We introduce generalized cubic partitions and discover the minimal excludant, as well as several additional results.
ER  -