# Problem 15E. Show with a Ferrers diagram that the number of partit...

## Transcribed Text

Problem 15E. Show with a Ferrers diagram that the number of partitions of n + k into k: parts equals the number of partitions of n into at most k: parts. (This is (15.2).) Many theorems about partitions can be proved easily by repre- senting each partition by a diagram of dots, known as a Ferrers diagram. Here we represent each term of the partition by a row of dots, the terms in descending order, with the largest at the top. Sometimes it is more convenient to use squares instead of dots (in this case the diagram is called a Young diagram by some authors but we shall use Ferrers diagram as the name for the figure). For example, the partition (5,4,2,1) of 12 is represented by each of the diagrams of Fig. 15.1. Figure 15.1

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

\$9.00
for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Combinatorics Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.