> #Weiji Zheng, Homework 25, 12/11/2020
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> #OK TO POST HOMEWORK
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> 
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> #Q1
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> #Draw the Ferrers diagram of the partition [9,6,5,3,1,1,1]. What is its conjugate partition?
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> 
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> #     * * * * * * * * *
> #     * * * * * *
> #     * * * * *
> #     * * *
> #     *
> #     *
> #     *
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> #     | | | | | | | | |
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> #    [7 4 4 3 3 2 1 1 1]
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> 
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> #Q2
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> #How many partitions of 151 are there with exactly 10 parts?

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> #pnk(151,10)
> #79811865

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> #Q3
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> #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])
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> 
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> # BZ([[6,5,3,1,1,1,1,1],-1])
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> #[[6, 4, 2, 2, 2, 2, 2], 0]
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> 
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> #Q4
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> #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?
> 
> #pnFast(10000)
> #36167251325636293988820471890953695495016030339315650422081868605887952568754066420592310556052906916435144
> #[seq(pnFast(i), i = 1 .. 10000)][10000]
> #36167251325636293988820471890953695495016030339315650422081868605887952568754066420592310556052906916435144
> #[seq(pnFast(i), i = 1 .. 20000)][20000]
> #252114813812529697916619533230470452281328949601811593436850314108034284423801564956623970731689824369192324789351994903016411826230578166735959242113097

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> 
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> #Q5
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> #Part of the problem with pnFast(n) is that the numbers get very big. Write a procedure
> #pnFastMod(n,m)
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> #that outputs p(n) mod m. What is
> 
> #pnFast(10^5,101)?
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> 
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> pnFastMod := proc(n, m) local i:
> pnFast(n) mod m:
> end:
> 
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> #pnFastMod(10^5, 101)
> #89

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