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. Cоmpute 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

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. Cоmpute 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

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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