(For other notation see Notation for the Special Functions.)
real variable. |
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nonnegative integers. |
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integer partition. |
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plane partition. |
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number of elements of a finite set . |
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divides . |
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greatest common divisor of positive integers and . |
The main functions treated in this chapter are:
binomial coefficient. |
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multinomial coefficient. |
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Eulerian number. |
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Gaussian polynomial. |
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Bell number. |
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Catalan number. |
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number of partitions of . |
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number of partitions of into at most parts. |
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number of plane partitions of . |
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Stirling numbers of the first kind. |
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Stirling numbers of the second kind. |
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).