# How to pronounce Stirling Numbers of Second Kind ${n\brace k}$?

The Stirling Numbers of the Second Kind, $${n\brace k}$$, count the number of ways to partition an $$n$$-element set into $$k$$ unlabeled non-empty parts and are rather useful for several introductory questions in combinatorics alongside the other earlier taught binomial coefficients $$\binom{n}{k}$$ and factorials, and so on.

The binomial coefficients have a standardized way of reading them aloud in English, being "$$n$$ choose $$k$$." Is there anything similar for Stirling Numbers of the Second Kind? Or for the Stirling Numbers of the First Kind?

In my head, when typing them out or thinking of them, I often read them with the TeX commands as "n brace k"... but if I were to try to use a more suggestive phrase that helps imply the meaning of the notation I might prefer "$$n$$ partition $$k$$" or "Second Stirling $$n$$ $$k$$."

I am curious how other people read this aloud in a classroom setting or in their own head.

• I was in fact thinking of asking you one of these days :) Sep 14, 2021 at 3:23
• For the Stirling numbers of the first kind, "$n$ cycle $k$" sounds very natural. I can't think of anything for ${n \brace k}$ which sounds anywhere near as good. Sep 14, 2021 at 4:38
• $n$ curly bracet $k$ is my favorite Sep 14, 2021 at 9:41

The book Concrete Mathematics by Graham, Knuth & Patashnik suggests “$$n$$ subset $$k$$” for $${n\brace k}$$ and “$$n$$ cycle $$k$$” for $${n \brack k}$$ (pp. 258–259 in the second edition).