6. Let P(n, k) denote the number of partitions of n into exactly k parts. Prove that P(n, k) = P(n − 1, k − 1) + P(n − k, k), for 1 ≤ k ≤ n. What are the initial conditions ? Compute P(9,3).
6. Let P(n, k) denote the number of partitions of n into exactly k parts. Prove that P(n, k) = P(n − 1, k − 1) + P(n − k, k), for 1 ≤ k ≤ n. What are the initial conditions ? Compute P(9,3).
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:6. Let P(n, k) denote the number of partitions of n into exactly k parts. Prove that
P(n, k) = P(n − 1, k − 1) + P(n − k, k), for 1 ≤ k ≤n. What are the initial conditions
? Compute P(9,3).
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