Question

7. Construct the generating functions for the number of partitions of n such that: a. No part is a multiple of 3 b. No part appears 3 or more times c. Show using algebra that the generating functions from parts a) and b) are equal.

          7. Construct the generating functions for the number of partitions of n such that:
a. No part is a multiple of 3
b. No part appears 3 or more times
c. Show using algebra that the generating functions from parts a) and b) are equal.

7. Construct the generating functions for the number of partitions of n such that:
a. No part is a multiple of 3
b. No part appears 3 or more times
c. Show using algebra that the generating functions from parts a) and b) are equal.

Added by Matthew L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Maitreya E

Step 1

We can have parts 1, 2, 4, 5, 7, 8, and so on. The generating function for this is: $$ G_1(x) = (1 + x)(1 + x^2)(1 + x^4)(1 + x^5)(1 + x^7)(1 + x^8) \cdots $$ Now, let's construct the generating function for the number of partitions of n such that no part Show more…

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Construct the generating functions for the number of partitions of n such that: a. No part is a multiple of 3 b. No part appears 3 or more times c. Show using algebra that the generating functions from parts a) and b) are equal.