Partitions in which every term but the smallest one is consecutive
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916173201801216 |
|---|---|
| author | Gupta, Rajat Lebowitz-Lockard, Noah |
| author_facet | Gupta, Rajat Lebowitz-Lockard, Noah |
| contents | 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 $n$ and an asymptotic formula for this quantity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partitions in which every term but the smallest one is consecutive Gupta, Rajat Lebowitz-Lockard, Noah Combinatorics Number Theory 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 $n$ and an asymptotic formula for this quantity. |
| title | Partitions in which every term but the smallest one is consecutive |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2403.15677 |