Fibonacci-like property of partition function

2023/08/10 by Qi-Yang Zheng, Zheng, Qi-Yang
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2308.06289

Abstract

The main result of the paper is the Fibonacci-like property of the partition function. The partition function p(n) has a property: p(n) ≤ p(n-1) + p(n-2). Our result shows that if we impose certain restrictions on the partition, then the inequality becomes an equality. Furthermore, we extend this result to cases with a greater number of summands.

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