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Permutations in a circle


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I came across a bit of a snag when I was working with permutations of things in a circle. The problem is that I have 8 particles, 4 negative, 4 positive(the particles are indistinguishable except by their charge) arranged in a circle. When I asked the question how many ways can I reorder these particles? I came up some interesting results.

 

According to the formula I was taught: (8-1)!/4!*4!

 

But this equals 8.75 permutations! Is this a special case? Is the formula wrong? Please help me out!

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I came across a bit of a snag when I was working with permutations of things in a circle. The problem is that I have 8 particles, 4 negative, 4 positive(the particles are indistinguishable except by their charge) arranged in a circle. When I asked the question how many ways can I reorder these particles? I came up some interesting results.

 

According to the formula I was taught: (8-1)!/4!*4!

 

But this equals 8.75 permutations! Is this a special case? Is the formula wrong? Please help me out!

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Well, nevermind, we didn't tackle a problem like that. We did a one where there was an alternating pattern, meaning postive then negative then positive... in a circle.

Does your problem have alternating positive/negative particles?

 

I lost the formula for alternating patterns on circular permutations.

 

However, I do remember one thing. Don't trust formulas :) , especially since mathematicians debate over this area of math.

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Well, nevermind, we didn't tackle a problem like that. We did a one where there was an alternating pattern, meaning postive then negative then positive... in a circle.

Does your problem have alternating positive/negative particles?

 

I lost the formula for alternating patterns on circular permutations.

 

However, I do remember one thing. Don't trust formulas :) , especially since mathematicians debate over this area of math.

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Well the formula I used was (n-1)!/x!*y! Where x and y the numbers of alike objects(indistinguishable). It is supposed to tell me how many possible different orders of particles I can have in a circle.

 

One of the permutations would be an alternating pattern.

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Well the formula I used was (n-1)!/x!*y! Where x and y the numbers of alike objects(indistinguishable). It is supposed to tell me how many possible different orders of particles I can have in a circle.

 

One of the permutations would be an alternating pattern.

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Because there are indistinguishable objects it works somewhat like a combination. The formula (I think) for indistinguishable permutations is n!/x! where x is the number of indistinguishable objects. You are taking away the permutations that look the same.

 

eg:

 

xxy xyx yxx

 

Its 3!/2!=3 not 3!=6 because xxy and xxy are the same even if the x's switch.

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Because there are indistinguishable objects it works somewhat like a combination. The formula (I think) for indistinguishable permutations is n!/x! where x is the number of indistinguishable objects. You are taking away the permutations that look the same.

 

eg:

 

xxy xyx yxx

 

Its 3!/2!=3 not 3!=6 because xxy and xxy are the same even if the x's switch.

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"Because there are indistinguishable objects it works somewhat like a combination. The formula (I think) for indistinguishable permutations is n!/x! where x is the number of indistinguishable objects. You are taking away the permutations that look the same.

 

eg:

 

xxy xyx yxx

 

Its 3!/2!=3 not 3!=6 because xxy and xxy are the same even if the x's switch."

 

That's true for linear permutations that repeat, I believe. I'm not sure it applies to circular permutations that repeat.

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"Because there are indistinguishable objects it works somewhat like a combination. The formula (I think) for indistinguishable permutations is n!/x! where x is the number of indistinguishable objects. You are taking away the permutations that look the same.

 

eg:

 

xxy xyx yxx

 

Its 3!/2!=3 not 3!=6 because xxy and xxy are the same even if the x's switch."

 

That's true for linear permutations that repeat, I believe. I'm not sure it applies to circular permutations that repeat.

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