Given n distinct objects, there are n ! permutations of the objects and n !

pachaquis3s

pachaquis3s

Answered question

2022-06-11

Given n distinct objects, there are n ! permutations of the objects and n ! / n "circular permutations" of the objects (orientation of the circle matters, but there is no starting point, so 1234 and 2341are the same, but 4321 is different).
Given т objects of k types (where the objects within each type are indistinguishable), r i of the i t h type, there are
n ! r 1 ! r 2 ! r k !
permutations. How many circular permutations are there of such a set?

Answer & Explanation

Aiden Norman

Aiden Norman

Beginner2022-06-12Added 16 answers

The generating function you want is
1 n d | n ( x 1 n / d + . . . + x k n / d ) d φ ( n d )
where the coefficient of x 1 r 1 . . . x k r k is the number you want.

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