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Guichard-Combinatorics-Graph-Theory
· Problem 1.8.7
Fundamentals
Mathematics — Probability · stirling-numbers
Problem
Prove:
S
(
n
,
k
)
=
∑
i
=
k
−
1
n
−
1
(
n
−
1
i
)
S
(
i
,
k
−
1
)
S(n,k) = \sum_{i=k-1}^{n-1} \binom{n-1}{i} S(i, k-1)
S
(
n
,
k
)
=
∑
i
=
k
−
1
n
−
1
(
i
n
−
1
)
S
(
i
,
k
−
1
)
.
Related theory
Stirling Numbers And Partition Functions
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