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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hi;

**We have the multiset**

**s ={1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 7, 7, 8, 9, 10, 10, 10, 10, 10}**

**and C has been busy trying to answer a question. So C brings it into the group because he thinks he has the right answer.**

**What is the number of partitions of s that add up to 17? C has an answer of 91.**

**A says) It is a lot higher than that C. A few minor mathematicians like De Moivre worked on these partition problems but it was finally the great Euler that told us everything about them. Incidentally, did I tell you fellows that the blood of Euler courses through my veins? Yes, I am related to him.**

**B says) It is lower not higher and why do you think De Moivre was a minor mathematician? Did you know that Newton would bring his probability problems to De Moivre?**

**C says) Those were handouts B and I had a hunch the answer was higher.**

**D says) Who is Euler?**

**E says) You are partially right C, Newton was trying to give him some work but only because he saw that he was great mathematician and Newton respected that. Also A, B is right, it is lower. Looks like all that Euler blood leaked out of you.**

**A says) It is higher bumpkin!**

**What do you say?**

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 461

Hello:

*Last edited by ElainaVW (2014-03-21 14:24:52)*

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What is a multiset? What do you mean by a partition of s?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

A multiset is used in combinatorics a lot. They are sometimes called families too. They are sets that are allowed to have duplicates.

A partition of a number is a way to write a number as a sum of other numbers.

1 + 5 = 6

1 + 1 + 4 = 6

1 + 2 + 3 = 6

Are all partitions of 6. They are similar to compositions except order does not count. 1 + 2 + 3 and 3 + 1 + 2 are considered to be the same.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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You explained partitions of a number. But what are partitions of a multiset? Are they subsets of it?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

They are like restricted partitions. The partitions must come from the multiset.

s ={1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 7, 7, 8, 9, 10, 10, 10, 10, 10}

1 + 1 + 1 + 1 + 2 + 2 + 8 is a restricted partition of 17 while

1 + 1 + 1 + 1 + 1 + 2 + 10 is not.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Are you asking to find the number of submultisets of s whose sum of elements is 17?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Yes but there is no need for the usage of that name, we call them partitions.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Did you notice something?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

I missed replying to a solution.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Is A claiming that Euler is a higher bumpkin.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

A is claiming something, I am not sure what it is.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Can we have A on the forum?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hmmmm, why do we want him?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hi gAr;

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Thanks!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

You are very welcome.

Have to go, see you later.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, see you later..

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hi gAr;

Did you know there is no analytical answer for anything more then a spread of 2?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,646

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hi ShivamS;

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,646

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,993

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,646

Wonderbar!

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