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Let Hk(n) be the number of vectors x1,...,xk for which

Chapter 1, Problem 15TE

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QUESTION:

Problem 15TE

Let Hk(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1 ≤ xin and x1 ≤ x2 ≤ ... ≤ xk.

(a) Without any computations, argue that

(b) Use the preceding recursion to compute H3(5).

Questions & Answers

QUESTION:

Problem 15TE

Let Hk(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1 ≤ xin and x1 ≤ x2 ≤ ... ≤ xk.

(a) Without any computations, argue that

(b) Use the preceding recursion to compute H3(5).

ANSWER:

Step 1 of 3

Let (n) be the number of vectors ....

(a) We have to prove that,

                                               (n)= n,

                                             (n) =  ( j ), k > 1

(b) we have to compute (5).

 

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