Question 3 Let An,k be the number of partitions P of the set {1,2,...n + 1} such that {k + 1} € P but for all j > k+1, {j} ¢ P. 1. Соmpute Ai,1- 2. Show that An.n is the nth Bell number B(n). 3. Show that An,k by An,k, then there are two important cases either {k} € P or {k} ¢ P. An,k-1 + An–1,k–1· Hint: If P is a partition counted n-.
Question 3 Let An,k be the number of partitions P of the set {1,2,...n + 1} such that {k + 1} € P but for all j > k+1, {j} ¢ P. 1. Соmpute Ai,1- 2. Show that An.n is the nth Bell number B(n). 3. Show that An,k by An,k, then there are two important cases either {k} € P or {k} ¢ P. An,k-1 + An–1,k–1· Hint: If P is a partition counted n-.
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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Transcribed Image Text:Question 3 Let Ank be the number of partitions P of the set {1,2,...n + 1}
such that {k + 1} € P but for all j > k + 1, {j} ¢ P.
1. Соmрute Ai,1.
2. Show that An.n is the nth Bell number B(n).
3. Show that An,k
by An.k, then there are two important cases either {k} € P_or {k} ¢ P.
An,k-1 + An-1,k–1· Hint: If P is a partition counted
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