For n, m Z+, let f(n, m) count the number of partitions of n where the
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4 = 2 + 2, 4 = 2+1 +1, 4 = l + l + l + l.
(a) Verify that for all n, m ∈ Z+,
f(n, m) = f(n - m, m) + f(n, m - 1).
(b) Write a computer program (or develop an algorithm) to compute f(n, m) for n, m ∈ Z+.
(c) Write a computer program (or develop an algorithm) to compute p(n), the number of partitions of a given positive integer n.
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a The partitions counted in fn m fall into two categories 1 Partitions where m is a summand These ar...View the full answer
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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