Enumeration of artitions with prescribed successive rank parity blocks

2017/03/22 by Seunghyun Seo, Seo, Seunghyun, Ae Ja Yee +1
Mathematics · #05A17 (Primary) 11P81 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1703.07507

openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Successive ranks of a partition, which were introduced by Atkin, are the difference of the ith row and the ith column in the Ferrers graph. Recently, in the study of singular overpartitions, Andrews revisited successive ranks and parity blocks. Motivated by his work, we investigate partitions with prescribed successive rank parity blocks. The main result of this paper is the generating function of partitions with exactly d successive ranks and m parity blocks.

Citations

• Overpartitions and singular overpartitions

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