Enumeration of odd-dimensional partitions modulo 4
Abstract
The number of standard Young tableaux on a partition shape \(\lambda\) is called the dimension of the partition. Partitions with odd dimensions were enumerated by McKay and were further characterized by Macdonald in the 1970s. 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 \(2\).
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Analytic Number Theory Research
Publication details
- Journal / source
- American Journal of Combinatorics
- Volume
- 5
- Pages
- 26–69
- Publication date
- 13 May 2026
- Language
- EN