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Sep 28, 2014, 6:58 pm # 1
Sep 29, 2014, 4:13 pm # 2
How many Partitions
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[ 9 posts ]
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ThePathOfWar
Posts: 139
1. The number 4 can be written as a sum of one or more natural
numbers in exactly five
ways: 4, 3+1, 2+1+1, 2+2, and 1+1+1+1 so 4 is said to have five
partitions. What is
the number partitions for the number 7?
2. Is there a nice formula to calculate the number of partitions
for any given any positive
integer ?
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aravindsidd
Posts: 163
Location: The internet
15 for 7
There is no nice formula, but there is an extremely accurate
approximation
for any there are approximately
partitions of .
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Sep 29, 2014, 6:48 pm # 3
Sep 29, 2014, 7:09 pm # 4
Sep 29, 2014, 8:15 pm # 5
Darn
Posts: 466
Location: The Endeavor
How does the above formula derive?
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The Endeavor
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ThePathOfWar
Posts: 139
Looks complicated to me.
_________________
I'm not bad in combinatorics, but I'm pathetic at everything
else. Therefore, my
understanding of combinatorics is limited.
I'm also pathetic at language arts. See here:
http://www.artofproblemsolving.com/Foru
... 8&t=609188
bobthesmartypants
Posts: 2245
Location:
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Complicated? Try this formula:
http://www.artofproblemsolving.com/Forum/code.php?hash=dadf29f8383ee2dab79f57737a4413e8823f0741&type=1&sid=417e34aba2908a1f0aebcdf0dd7a5839
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Sep 30, 2014, 5:12 am # 6
Sep 30, 2014, 5:19 am # 7
where
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That's it, I've found it. This infinite series is indeed
detergent.
donot
Posts: 179
Location: Varies with
location.
And I don't want to calculate ...
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aravindsidd
Posts: 163
Location: The internet
The formula is derived using some advanced topics so you may
just want to just google
"Partition function", and if you are interested in this kind of
stuff I encourage to go
further and expand your knowledge! (Also note the formula is
only an approximation,
that happens to work well.)
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Prove: That I need AOPS' Introduction to English.
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Sep 30, 2014, 7:54 am # 8
Sep 30, 2014, 9:03 am # 9
ThePathOfWar
Posts: 139
bobthesmartypants wrote:
Complicated? Try this formula:
where
Bah! Humbug! Ok here. I'll ask for something more reasonable.
Are there any nice
relations between partitions that may help us be able to find
the number of partitions in
a number?
_________________
I'm not bad in combinatorics, but I'm pathetic at everything
else. Therefore, my
understanding of combinatorics is limited.
I'm also pathetic at language arts. See here:
http://www.artofproblemsolving.com/Foru
... 8&t=609188
Pengu2005
Posts: 83
Look up Ferrer's Diagram.
_________________Hmm I guess I'll bandwagon and post goals (it
seems to be quite a popular trend)
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