{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ass3-v2-qn

# ass3-v2-qn - Math 239 Assignment 3 Due Friday noon May 27...

This preview shows pages 1–2. Sign up to view the full content.

Due: Friday noon, May 27. Each question carries 20 marks. Math 239 Assignment 3 1. How many nonnegative integers smaller than 100,000 have the sum of their digits equal to 23? 2. Consider compositions of a positive integer n into 2 positive parts. (a) Define an appropriate set S 1 and write down a generating function Φ S 1 ( x ) to count the number of compositions n = c + d with c < d . Express your answer as a rational function. (b) Define another appropriate set S 2 and write down another generating function Φ S 2 ( x ) to count the number of compositions n = e + f with even e and arbitrary f . Express your answer as a rational function. (c) Suppose Φ S 1 ( x ) = n 1 a n x n and Φ S 2 ( x ) = n 1 b n x n . Use your answers in (a) and (b) to show that n a n = b n . Express a n in terms of n . (d) For each n , let S 1 n and S 2 n be the respective subsets of S 1 and S 2 containing the compo- sitions of n . Establish a bijection between S 1 n and S 2 n (which maps any ( c , d ) S 1 n to some ( e , f ) S 2 n ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

ass3-v2-qn - Math 239 Assignment 3 Due Friday noon May 27...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online