An overpartition analogue of Bressoud conjecture for even moduli

2023/12/01 by Y. H. Chen, Tiancheng Gu, Chen, Y. H. +7
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2312.00466

openalex publication_date 2023/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1980, Bressoud conjectured a combinatorial identity A_j=B_j for j=0 or 1. In this paper, we introduce a new partition function B₀ which can be viewed as an overpartition analogue of the partition function B₀. An overpartition is a partition such that the last occurrence of a part can be overlined. We build a bijection to get a relationship between B₀ and B₁, based on which an overpartition analogue of Bressoud's conjecture for j=0 is obtained.

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