# §26.1 Special Notation

(For other notation see Notation for the Special Functions.)

 real variable. nonnegative integers. integer partition. plane partition. number of elements of a finite set . divides . greatest common divisor of positive integers and .

The main functions treated in this chapter are:

 binomial coefficient. multinomial coefficient. Eulerian number. Gaussian polynomial. Bell number. Catalan number. number of partitions of . number of partitions of into at most parts. number of plane partitions of . Stirling numbers of the first kind. Stirling numbers of the second kind.

## ¶ Alternative Notations

Many combinatorics references use the rising and falling factorials:

26.1.1

Other notations for , the Stirling numbers of the first kind, include (Abramowitz and Stegun (1964, Chapter 24), Fort (1948)), (Jordan (1939), Moser and Wyman (1958a)), (Milne-Thomson (1933)), (Carlitz (1960), Gould (1960)), (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)).

Other notations for , the Stirling numbers of the second kind, include (Fort (1948)), (Jordan (1939)), (Moser and Wyman (1958b)), (Milne-Thomson (1933)), (Carlitz (1960), Gould (1960)), (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)), and also an unconventional symbol in Abramowitz and Stegun (1964, Chapter 24).