INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

March 15, 2021

What is Stirling Number of First Kind

We will learn about a combinatorics tool: Stirling Numbers of First Kind. Here is a video to get you started.

Problem 1

Show that
$$
s(r, n)=s(r-1, n-1)+(r-1) s(r-1, n)
$$
where $r, n \in \mathbf{N}$ with $n \leq r$

Problem 2

Show the following:

$$ s(r, 0)=0 \text { if } r \geq 1 $$

$$ s(r, r)=1 \text { if } r \geq 0 $$

$$ s(r, 1)=(r-1)! \text { for } r \geq 2 $$

$$ s(r, r-1)={{r} \choose {2}} $$

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
enter