Problem 5: Let pr(n) be the number of integer partitions of n into k parts. Showthat1Pr(n) >nk! (k – 1-Deduce that the total number p(n) of partitions of n grows faster (as n → 0) thanany polynomial function of n. (Hint: It is enough to show that, for any fixed k, wehave p(n) > nk for sufficiently large n.)

Name: Problem 5: Let pr(n) be the number of integer partitions of n into k
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Description: Problem 5: Let pr(n) be the number of integer partitions of n into k parts. Showthat1Pr(n) >nk! (k – 1-Deduce that the total number p(n) of partitions of n grows faster (as n → 0) thanany polynomial function of n. (Hint: It is enough to show that, f

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that 1 Pr(n) > n k! (k – 1 | Deduce that the total number p(n) of partitions of n grows faster (as n → ) than any polynomial function of n. (Hint: It is enough to show that, for any fixed k, we have p(n) > nk for sufficiently large n.)

that 1 Pr(n) > n k! (k – 1 | Deduce that the total number p(n) of partitions of n grows faster (as n → ) than any polynomial function of n. (Hint: It is enough to show that, for any fixed k, we have p(n) > nk for sufficiently large n.)

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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Problem 5: Let pr(n) be the number of integer partitions of n into k parts. Show
that
1
Pr(n) >
n
k! (k – 1
-
Deduce that the total number p(n) of partitions of n grows faster (as n → 0) than
any polynomial function of n. (Hint: It is enough to show that, for any fixed k, we
have p(n) > nk for sufficiently large n.)

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