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arXiv · 2610.34155

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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Suverchla Arora, Meenakshi Rana, Shruti Sharma, Nilanjan Bag. 2026-10-25. Colored Partitions and Minimal Excludants. https://arxiv.org/abs/2610.34155

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