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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.

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    $\begingroup$ I was in fact thinking of asking you one of these days :) $\endgroup$
    – Math Lover
    Sep 14, 2021 at 3:23
  • $\begingroup$ 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. $\endgroup$ Sep 14, 2021 at 4:38
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    $\begingroup$ $n$ curly bracet $k$ is my favorite $\endgroup$ Sep 14, 2021 at 9:41

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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).

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