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). Show that for the Bell numbers B(n) that B(n) – B(n – 1) – B(n – 2) is always an even number. Conclude that B(n) is even exactly when n is one less than a multiple of 3. Hint: For a set partition A of [n] consider interchanging which sets n and n – 1 are in. This gives you a way of pairing up most of the set partitions of [n].

). Show that for the Bell numbers B(n) that B(n) – B(n – 1) – B(n – 2) is always an even number. Conclude that B(n) is even exactly when n is one less than a multiple of 3. Hint: For a set partition A of [n] consider interchanging which sets n and n – 1 are in. This gives you a way of pairing up most of the set partitions of [n].

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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). Show that for the Bell numbers B(n) that B(n) – B(n – 1) – B(n – 2) is always an even number. Conclude that B(n) is even exactly when n is one less than a multiple of 3. Hint: For a set partition A of [n] consider interchanging which sets n and n – 1 are in. This gives you a way of pairing up most of the set partitions of [n].
Transcribed Image Text:). Show that for the Bell numbers B(n) that B(n) – B(n – 1) – B(n – 2) is always an even number. Conclude that B(n) is even exactly when n is one less than a multiple of 3. Hint: For a set partition A of [n] consider interchanging which sets n and n – 1 are in. This gives you a way of pairing up most of the set partitions of [n].
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