Enumeration of Even Dimensional Partitions modulo 4

2025/11/15 by Aditya Khanna, Khanna, Aditya
Mathematics · #05A17 (primary) #20C30 (secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2511.11977

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

The number of standard Young tableaux possible of shape corresponding to a partition λ is called the dimension of the partition and is denoted by f^λ. Partitions with odd dimensions were enumerated by McKay and were further characterized by Macdonald using the theory of 2-core towers. We use the same theory to extend the results to partitions of n with dimensions congruent to 2 modulo 4 which are enumerated by a₂(n). We provide explicit results for a₂(n) when n has no consecutive 1s in its binary expansion and give a recursive formula to compute a₂(n) for all n.

Citations

• Spinorial Representations of Symmetric Groups
• Determinants of Representations of Coxeter Groups

Related

• Enumeration of Odd Dimensional Partitions modulo 4
• Enumeration of partitions via socle reduction
• Identities involving partitions with distinct even parts and 4-regular partitions
• Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4
• Congruences and density results for partitions into distinct even parts