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November 14th, 2013, 04:25 AM   #1
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transpositions of a set - terms and notations

Hello All,

I have 8 elements that are sequentially are connected as below making a circle :

P -> R -> G -> B -> O -> S -> C -> D -> P

We have to list all possible 5-transposition orders i.e.

dO : G -> B -> O -> S -> C
dS : B -> O -> S -> C -> D
.
.
.
dP : C -> D -> P -> R -> G

Given that, I have the following questions:
a) What statistical terms and notations are used to describe this problem?
b) What is the appropriate / standard form of writing above sets?
c) What is the general formula to calculate the number of all possible such transpositions?

Best,
David
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