A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences
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 $n\geq33$ and that certain second $j$-shifted difference of $u(n)$ are positive.
Fields of Study & Subjects
graph theory and CDMA systems
Mathematical Approximation and Integration
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Advances in Applied Mathematics
- Volume
- 180
- Pages
- 103133–103133
- Publication date
- 21 July 2026
- Language
- EN