About the Project

Stirling cycle numbers

AdvancedHelp

(0.002 seconds)

3 matching pages

1: 26.13 Permutations: Cycle Notation
β–ΊThe number of elements of 𝔖 n with cycle type ( a 1 , a 2 , , a n ) is given by (26.4.7). β–ΊThe Stirling cycle numbers of the first kind, denoted by [ n k ] , count the number of permutations of { 1 , 2 , , n } with exactly k cycles. … β–Ί
26.13.3 [ n k ] = | s ⁑ ( n , k ) | .
2: 4.13 Lambert W -Function
β–ΊFor the definition of Stirling cycle numbers of the first kind [ n k ] see (26.13.3). … β–Ί
4.13.10 W k ⁑ ( z ) ξ k ln ⁑ ξ k + n = 1 ( 1 ) n ξ k n ⁒ m = 1 n [ n n m + 1 ] ⁒ ( ln ⁑ ξ k ) m m ! ,
β–Ί
4.13.11 W ± 1 ⁑ ( x βˆ“ 0 ⁒ i ) Ξ· ln ⁑ Ξ· + n = 1 1 Ξ· n ⁒ m = 1 n [ n n m + 1 ] ⁒ ( ln ⁑ Ξ· ) m m ! ,
3: 26.8 Set Partitions: Stirling Numbers
β–Ί s ⁑ ( n , k ) denotes the Stirling number of the first kind: ( 1 ) n k times the number of permutations of { 1 , 2 , , n } with exactly k cycles. …