Question 1
Draw the Ferrers diagram of the partition [9,6,5,3,1,1,1]. What is its conjugate partition?

Answer 1
[9,6,5,3,1,1,1]
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To find the conjugate we look at the stars in vertical order

we get [7, 4, 4, 3, 3, 2, 1, 1, 1]

Question 2
How many partitions of 151 are there with exactly 10 parts?

Answer 2:
We can use pnk(151, 10) to find this
We get 79811865 partitions 

Question 3
Read and understand this gem. By hand, find the image of
[[6,5,3,1,1,1,1,1],-1]

Check it against BZ([[6,5,3,1,1,1,1,1],-1])

Answer 3
BZ([[6,5,3,1,1,1,1,1],-1])
[[6, 4, 2, 2, 2, 2, 2], 0]

Question 4
If you want to find the number of partitions of 10000 using procedure pnFast in M24.txt and you type,
pnFast(10000);

You would get an error message. Why?

But if you do

[seq(PnFast(i),i=1..10000)][10000];

you would get the answer. Why?

Use this way to find the number of partitions of 20000. How far can you get?

Answer 4
pnFast is a recurusce function and having 10000 layers of recursion is too much but if you calculate all the levels before maple remembers it and uses it

seq(pnFast(i),i=1..20000)[20000]

252114813812529697916619533230470452281328949601811593436850314108034284423801564956623970731689824369192324789351994903016411826230578166735959242113097

Question 5
Part of the problem with pnFast(n) is that the numbers get very big. Write a procedure
pnFastMod(n,m)

that outputs p(n) mod m. What is

pnFast(10^5,101)?

Answer 5
pnFastMod:=proc(n, m) local i, j:
i:=pnFast(n) mod m:
i:
end proc:
pnFastMod(100000,101)

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