Problem 5: Let pr(n) be the number of integer partitions of n into k parts. Show that Pr(n) > k! (k Deduce that the total number p(n) of partitions of n grows faster (as n → o) than any polynomial function of n. (Hint: It is enough to show that, for any fixed k, we have p(n) > n* for sufficiently large n.) Problem 6: Let n be a positive integer. Prove that we have the inequality of partition numbers p(n)² < p(n² + 2n).

Problem 5: Let pr(n) be the number of integer partitions of n into k parts. Show that Pr(n) > k! (k Deduce that the total number p(n) of partitions of n grows faster (as n → o) than any polynomial function of n. (Hint: It is enough to show that, for any fixed k, we have p(n) > n* for sufficiently large n.) Problem 6: Let n be a positive integer. Prove that we have the inequality of partition numbers p(n)² < p(n² + 2n).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

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