A partition of a positive integer n is a way to write n as a sum of
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Question:
A partition of a positive integer n is a way to write n as a sum of positive integers where the order of terms in the sum does not matter. For instance, 7 = 3 + 2+1 + 1 is a partition of 7. Let Pm equal the number of different partitions of m, and let Pm,n be the number of different ways to express m as the sum of positive integers not exceeding n.
a) Show that Pm,n = Pm.
b) Show that the following recursive definition for Pm,n is correct:
c) Find the number of partitions of 5 and of 6 using this recursive definition.
Related Book For
College Algebra
ISBN: 978-0134697024
12th edition
Authors: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
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