Partitions in which every term but the smallest one is consecutive
Combinatorics
2024-03-26 v1 Number Theory
Abstract
In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smallest one. We find formulas relating to the smallest parts of consecutive and almost consecutive partitions. We also find an alternate combinatorial interpretation of the number of almost consecutive partitions of a given integer and an asymptotic formula for this quantity.
Cite
@article{arxiv.2403.15677,
title = {Partitions in which every term but the smallest one is consecutive},
author = {Rajat Gupta and Noah Lebowitz-Lockard},
journal= {arXiv preprint arXiv:2403.15677},
year = {2024}
}