Proof of a conjecture of Lundow and Rosengren on the bimodality of -binomial coefficients

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• 作者：Xun-Tuan Su^a ; ^{suxuntuan@yahoo.com.cn} ; Yi Wang^b ; ^{wangyi@dlut.edu.cn}
• 关键词：Unimodality ; Bimodality ; p ; q-binomial coefficients
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 July, 2012
• 卷：391
• 期：2
• 页码：653-656
• 文件大小：109 K

摘要

Lundow and Rosengren observed that the magnetization distributions of Ising model are remarkably well-fitted by the -binomial distributions based on an assumption that the -binomial distribution is unimodal or bimodal. In the present paper we show that this assumption holds for all positive numbers p and q.