Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Prove inequality:

$ S(n,k-1)\cdot S(n,k+1) \le (S(n,k))^2 $

for $n,k\in\mathbb{N}$, where $S(n,k)$ is the Stirling number of the second kind.

I think induction is the last resort. I don't know if it will work but I rather want to avoid it.

share|cite|improve this question
A google search with the keywords "Stirling numbers" and "log-concave" gives several hits, like and… . –  darij grinberg Mar 9 '12 at 18:02
Asked and answered at,… - voting to close. –  Gerry Myerson Mar 10 '12 at 4:46
@darij grinberg I don't understand why in the inductive step is on $n$. Why does it work.. –  xan Mar 10 '12 at 13:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.