Positivity and tails of pentagonal number series

2024/03/10 by Nian Hong Zhou, Zhou, Nian Hong · 1 citation
Mathematics · #11F27 #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Primary 05A30 #Secondary 05A15

paper · pdf · doi:10.48550/arxiv.2403.06196

openalex publication_date 2024/03/10 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we refine a result of Andrews and Merca on truncated pentagonal number series. Subsequently, we establish some positivity results involving Andrews--Gordon--Bressoud identities and d-regular partitions. In particular, we prove several conjectures of Merca and Krattenthaler--Merca--Radu on truncated pentagonal number series.

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• Proof of a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of M_C1(m,n) and M_C5(m,n)

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