A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences

2025/05/21 by Banerjee, Koustav, Bringmann, Kathrin, Kane, Ben
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.15236

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 Turán inequalities for n≥33 and that certain second j-shifted difference of u(n) are positive.

Citations

• Log-concavity for unimodal sequences
• Log-concavity for partitions without sequences
• A Rademacher-type exact formula for partitions without sequences
• Fourier Coefficients of Weight Zero Mixed False Modular Forms
• Higher Turán inequalities for the plane partition function
• The second shifted difference of partitions and its applications
• THE SECOND SHIFTED DIFFERENCE OF PARTITIONS AND ITS APPLICATIONS
• Turán inequalities for the plane partition function
• Fractional partitions and conjectures of Chern-Fu-Tang and\n Heim-Neuhauser
• Exact Formulae for the Fractional Partition Functions
• A Framework for Modular Properties of False Theta Functions
• Higher Order Turán Inequalities for the Partition Function
• Log-Concavity of the Partition Function

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