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arXiv · 2505.15236

A generic approach to proving Tur\'{a}n-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences

Koustav Banerjee·Kathrin Bringmann·Ben Kane
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Abstract

We derive an asymptotic expansion with effective error bound for $u(n)$, counting the number of unimodal sequences of size $n$. We prove that $u(n)$ satisfies the higher order Tur\'{a}n inequalities for $n\geq33$ and that certain second $j$-shifted difference of $u(n)$ are positive.

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Koustav Banerjee, Kathrin Bringmann, Ben Kane. 2025-05-21. A generic approach to proving Tur\'{a}n-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences. https://arxiv.org/abs/2505.15236

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