(9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts is a k-tuple (a₁,..., ak) of nonnegative integers such that a₁ + . . . + ak = n, while a (strong) composition of n into k parts is the same except a₁,..., a have to be positive integers. Find a bijection between the set of weak compositions of n into k parts and the set of strong compositions of n + k into k parts.
(9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts is a k-tuple (a₁,..., ak) of nonnegative integers such that a₁ + . . . + ak = n, while a (strong) composition of n into k parts is the same except a₁,..., a have to be positive integers. Find a bijection between the set of weak compositions of n into k parts and the set of strong compositions of n + k into k parts.
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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Transcribed Image Text:(9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts is a
k-tuple (a₁,..., ak) of nonnegative integers such that a₁ + ... + ak = n, while a (strong)
composition of n into k parts is the same except a₁, ..., a have to be positive integers.
Find a bijection between the set of weak compositions of n into k parts and the set of strong
compositions of n + k into k parts.
(10) A student wants to distribute 15 hours of work across 7 days of the week so that they are working
an integer amount of hours each day. However, they also want to have exactly two days of the week
with no work. How many ways can they do this?
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