





















Abstract:The number of standard Young tableaux of shape a partition $\lambda$ is called the dimension of the partition and is denoted by $f^{\lambda}$. Partitions with odd dimensions were enumerated by McKay and were further characterized by Macdonald. Let $a_i(n)$ be the number of partitions of $n$ with dimension congruent to $i$ modulo 4. In this paper, we refine Macdonald's and McKay's results by computing $a_1(n)$ and $a_3(n)$ when $n$ has no consecutive 1s in its binary expansion or when the sum of binary digits of $n$ is 2.
| Comments: | 40 pages; improved exposition |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05E10 (Primary), 20C30 (secondary) |
| Cite as: | arXiv:2207.07513 [math.CO] |
| (or arXiv:2207.07513v4 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2207.07513 arXiv-issued DOI via DataCite |
|
| Journal reference: | Amer. J. Comb. 5 (2026) 26 - 69 |
| Related DOI: | https://doi.org/10.63151/amjc.v5i.30
DOI(s) linking to related resources |
From: Aditya Khanna [view email]
[v1]
Fri, 15 Jul 2022 14:57:38 UTC (27 KB)
[v2]
Thu, 24 Aug 2023 05:57:15 UTC (28 KB)
[v3]
Sat, 15 Nov 2025 01:06:51 UTC (21 KB)
[v4]
Sun, 24 May 2026 20:33:45 UTC (41 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。