N. Guru Sharan, Armin Straub — Preprint — 2025
Abstract
A well-studied statistic of an integer partition is the size of its Durfee square. In particular, the number \(D_k(n)\) of partitions of \(n\) with Durfee square of fixed size \(k\) has a well-known simple rational generating function. We study the number \(R_k(n)\) of partitions of \(n\) with Durfee triangle of size \(k\) (the largest subpartition with parts \(1, 2, \ldots, k\)). We determine the corresponding generating functions which are rational functions of a similar form. Moreover, we explicitly determine the leading asymptotic of \(R_k(n)\), as \(n \to \infty\).Download
| Link | Size | Description | Hits |
|---|---|---|---|
| partitions-durfee-triangles.pdf | 324.62 KB | Preprint (PDF, 21 pages) | 19 |
BibTeX
@article{partitions-durfee-triangles-2025,
author = {N. Guru Sharan and Armin Straub},
title = {Partitions with Durfee triangles of fixed size},
journal = {Preprint},
year = {2025},
}