Definition:Stirling Numbers of the First Kind/Notation
Jump to navigation
Jump to search
Definition
The notation $\ds {n \brack k}$ for the unsigned Stirling numbers of the first kind is that proposed by Jovan Karamata and publicised by Donald E. Knuth.
The notation $\map s {n, k}$ for the signed Stirling numbers of the first kind is similar to variants of that sometimes given for the unsigned.
Usage is inconsistent in the literature.
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