Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity

2024/05/31 by Cristina Ballantine, Amanda Welch, Ballantine, Cristina +1 · 1 citation
Chemistry · Mathematics · #05A17 #05A20 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #History and advancements in chemistry #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.00139

openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the number of various partitions of n with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for n≥ 5 we have p_od^eu(n)

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• Combinatorial proof of an inequality on some partitions separated by parity

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