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1. The Bell number B(n) is the number of all set partitions of [n] = {1,..., n}, regardless of size. In other words, B(n) = Σk-1 S(n, k). Prove the following identity: n = Σ (7) B(₁ B(i) i=0 B(n + 1) = Σ

1. The Bell number B(n) is the number of all set partitions of [n] = {1,..., n}, regardless of size. In other words, B(n) = Σk-1 S(n, k). Prove the following identity: n = Σ (7) B(₁ B(i) i=0 B(n + 1) = Σ

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Combinatorics
1. The Bell number B(n) is the number of all set partitions of [n] = {1,..., n}, regardless of size. In other words, B(n) = 1 S(n, k). Prove the following identity: B(n+1)=Σ () B n B(i)
Transcribed Image Text:1. The Bell number B(n) is the number of all set partitions of [n] = {1,..., n}, regardless of size. In other words, B(n) = 1 S(n, k). Prove the following identity: B(n+1)=Σ () B n B(i)
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