Definition:Stirling Numbers of the Second Kind/Notation
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Definition
The notation $\ds {n \brace k}$ for Stirling numbers of the second kind is that proposed by Jovan Karamata and publicised by Donald E. Knuth.
Other notations exist.
Usage is inconsistent in the literature.
Technical Note
The $\LaTeX$ code for \(\ds {n \brace k}\) is \ds {n \brace k} .
The braces around the n \brace k are important.
The \ds is needed to create the symbol in its proper house display style.
Sources
- 1935: Jovan Karamata: (On notation styles for Stirling Numbers -- title TBC) (Mathematica (Cluj) Vol. 9: pp. 164 – 178)
- 1992: Donald E. Knuth: Two Notes on Notation (Amer. Math. Monthly Vol. 99: pp. 403 – 422) www.jstor.org/stable/2325085
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients