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arXiv · 2606.29884

A sharper log-convexity inequality for Bell numbers

Vuong Bui
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Abstract

We prove a stronger version of the log-convexity inequality for the Bell numbers $B_n$. In particular, for $n\ge 5$, we have \[ B_{n+1}B_{n-1} - (B_n)^2 \ge \sum_{i=1}^{n} F_i (B_{n-i})^2, \] where $F_i$ is the $i$-th Fibonacci number with $F_0=F_1=1$. The simple proof is mostly combinatorial with elementary inequalities.

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Vuong Bui. 2026-06-29. A sharper log-convexity inequality for Bell numbers. https://arxiv.org/abs/2606.29884

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