基于概率统计方法证明若干组合恒等式
Proofs of Several Combinatorial Identities Based on Probability Statistics Method
DOI: 10.12677/AAM.2024.131015, PDF,    科研立项经费支持
作者: 徐 晨, 常桂松：东北大学理学院数学系，辽宁 沈阳
关键词: 组合等式；负二项分布；Bell多项式；Combinatorial Identity； Negative Binomial Distribution； Bell Polynomial
摘要: 组合恒等式的发现与证明一直是组合数学的一个主要分支，一些组合等式因其复杂性难以直接证明，如何给出组合恒等式的简洁证明是组合数学的重要研究方向。本文应用负二项分布卷积的不同表达形式，与负二项分布的可加性等性质，发现并证明了若干组合恒等式。
Abstract: Finding and proving combinatorial identities is an important part of combinatorial mathematics. However, some combinatorial identities contain computational complexity, which hinders the direct proofs. So it is an important research direction in combinatorial mathematics to give concise proofs of combinatorial identities. In this paper, some combinatorial identities are found and proved by using different expressions of convolution of negative binomial distribution and the additivity of negative binomial distribution.
文章引用：徐晨, 常桂松. 基于概率统计方法证明若干组合恒等式[J]. 应用数学进展, 2024, 13(1): 127-132. https://doi.org/10.12677/AAM.2024.131015

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