Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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Restricted permutation of a ordered set with subsets

I have an ordered set, with three subsets; S = (A={1, 5}, B={3, 6}, C={8}). I currently want to figure out how many permutations there are if each permutation step is restricted by subset A or B swapping an element with subset C. While I can figure…
anders fylling
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Calculating permutations for multiple questions and responses

We are administering a survey and trying to determine how many permutations exist for the combination of question numbers and and responses in order to check our work. Specifically, we have a set of three survey questions, and four possible…
FBRK_21
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Permutation vs Variation - To rank 3 people

I am new to permutation and combination and am looking for guidance in the following example: We have 3 people - A, B, C How many ways are there to arrange them into Rank 1,2,3 Looking at the example, it is clear that No repetitions are allowed and…
variable
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Number of $k$-cycles in permutations of $[2k]$?

What is the expectation of the number of $k$-cycles in a randomly selected permutation of $[2k] = {1,2, . . . ,2k}$?
skd
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How many possible cases are there

I'm a dentist with biiiig gaps in my math. People have normally 32 teeth. If we say any random tooth or teeth can be extracted, what are the different possible cases (is it called permutations?) Are there? Someone can have all 32 teeth present…
Wael Kassab
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Calculate all permutations where first and last element of the set are not changed.

I am writing code to calculate all the permutations of a list and for the sake of optimization, would like to find an algorithm which generates permutations without changing the first and last element of my…
Christian Nebe
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Permutations: Notation that uses composition with exponents?

Notation question. Wiki Compositions of permutations claims that compositions : $$\sigma \bullet \pi$$ is the function that maps any element $x$ of the set to: $$\sigma (\pi (x))$$ and that another notation for permutations is denoted by an…
user644059
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Number of partitions of list

If I have my_list = [0, 1, 2]. I want to figure out how many possible list partitions there are for a list of length $n$. For the above example, there would be: [[0, 1, 2]] [[0, 1], [2]] [[0], [1, 2]] [[0], [1], [2]]
Harry Stuart
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Simplifying permutations written in cycle notation

I was wondering how I could simplify $((1 3 5)(2 3 4 1)(3 2 1))^{−1}$. I was going to simplify the inner bracket section first then apply the inverse but I am having trouble simplifying it. I see that $1\to3\to5\to1 $ but also $1\to3\to4\to1$…
user635953
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finding $n$ from two permutations.

${^np_4=\ 5(^np_4)}$ I can't find the value of n. What I have done: ${\frac{n!}{(n-4)!}=\ 5\left(\frac{n!}{(n-4)!}\right)}$ ${\frac{n(n-1)(n-2)(n-3)(n-4)!}{(n-4)!}=\ 5\frac{n(n-1)(n-2)(n-3)(n-4)!}{(n-4)!}}$ ${n(n-1)(n-2)(n-3)=\…
Hadaf
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Letters Permutation and eliminate some option

There are 5 letters A,B,C,D and E. How many permutations are possible of these 5 letters if AB , BC , CD & DC are not allowed ? I am very thankful to you if you solve this problem for me and tell me a proper way to solve it.
Aashish
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Decomposing a permutation

Let $g ∈ S_n$ be a permutation. Describe a method for answering the following question: does there exist a permutation $f ∈ S_n$ such that $f ◦ f = g$? I don't want to be spoonfed the answer, but can someone give me a direction? It is getting late…
user600210
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How many configurations are in a 16 by 16 grid filled with colors?

What I am asking is the amt of possible configurations of a 16x16 sprite? I tried doing the following by myself I just want to know if I'm correct. I think if I have RGB as color it would be $256 \cdot 256 \cdot 256$ which is $256^3$…
Prolight
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(GR. 10) 10 people are to be seated in a row. What is the total number of ways if...

Please help me! I understand what the question is asking for, but I can’t seem to get the right answer. The correct no. of ways should be $645,120$, though that may be incorrect. If anyone is kind enough to show me the solution, I would be very…
ahhh
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