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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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How can I solve an equation with permutations using their disjoint cycles?

I've got a permutation $S$ and I need to find out all the permutations $R$ with: $R \circ R = S$. How can I solve it using its product of disjoint cycles? I know how to solve such an equation,but using letters and trying every case. But this…
flaviumanica
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Is there a name for these oscillations in the self-similarity of a set under the action of a cyclic group?

I don't know much about group theory and card-shuffling theory, so this may already have a name I don't know about. I often shuffle a deck of cards using a method that is defined by a particular element of $S_{52}$, the symmetric group on 52…
DumpsterDoofus
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Problem on circular permutation

In how many ways can $x$ people be seated at a round table so that all will not have the same neighbours in any two arrangements?
Hitawari Kai
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Product of $2$ permutations

$(2,3)(4,6,5,1,2)=?$ The multiplication is from right to left. I don't know, where I make the mistake. Denote $\tau=(2,3), \sigma=(4,6,5,1,2)$ $1\ \ 2\ \ 3\ \ 4\ \ 5\ \ 6$$\quad$ first apply $\sigma$ $2\ \ 4\ \ 3\ \ 6\ \ 1\ \ 5$$\quad$ then…
inequal
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Permutations and combinations - number of ways to pay

Question: 22 people go to a movie theater. 11 of them are carrying a 50 dollar bill while the other 11 are carrying a 100 dollar bill. The ticket for the movie theater costs $50. The cashier initially has no money. In how many ways can the 22…
Gummy bears
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Permutations and combinations - choosing an integer

Question: In how many ways can we choose 2 distinct integers from 1 to 100 such that the difference between them is at most 10? Approach: I tried to fix a certain number, and then find the number of integers that would satisfy the condition…
Gummy bears
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Permutations and combinations - number of solutions

Question: Find the number of solutions of $x_1+x_2+x_3 = 51$ for $x_1,x_2,x_3$ being odd numbers Not sure how I would even begin this question. It would be simple except for the condition given of being odd numbers. Please help by giving a hint to…
Gummy bears
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Every solution of a permutation equation?

I have the three permutations $$a=(1\;3\;4\;8),\quad b=(2\;3\;5\;7),\quad c=(4\;3\;2\;8)$$ and I have to find all $x$ satisfying $$axb=c.$$ I have found one solution (I hope it's good): $$x=(7\;5\;1\;8\;3\;2)$$ Now my problem is, that the task says…
Seasharp
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Calculating Permutations of multiple, non-equal shapes on 2-Dimensional grid

I originally posted this in StackOverflow before finding this Mathematics forum. This is primarily a mathematics question so I am reposting here: Situation: The following components exist for this problem: Two-dimensional, rectangular grid ("r"…
AWaddington
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The order of a cyclic subgroup, generated by a permutation

I was wondering, how can I prove that all cyclic subgroups generated by a permutation, has the same order as the permutation? For example, cyclic subgroup $\langle(---)\rangle$ will have order 3. So far, my text book haven't given a proof for this,…
JustDanyul
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A question on colouring cubes

We are given 6 distinct colours and a cube.We have to colour each face with one of the six colours and two faces with a common edge must be coloured with different colours.How many distinct colouring ways are there?
lokesh sangabattula
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Permutation of N items taken 1,2,3…N at a time.

I want to know the formula for the following: 1.) Permutation of N different items taken 1,2,3...N at a time. 2.) Permutation of N items taken 1,2,3...N at a time but with repeating items. I couldn't search this in the internet. I tried to derive…
Creol
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Prove that K is subgroup.

Let K be the set of all permutations of $ S_4 $ type $ [2 ^ 2] $ and the identity permutation $\in K $. Prove that $ K $ is a subgroup $ S_4 $. I would like to prove that for$\pi, p \in S_4$ and type of $[2^2]$ $\pi p $ also is in K. But I can't…
user180834
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Permutations with forbidden values

I already asked this question in the mathoverflow forums, but it seems I won't get an answer as fast as I need one. So I'm moving the thread here. Besides, maybe it isn't as hard as to post it there. This question has some references to programming…
SmeltQuake
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How to calculate this permutaion problem

In how many ways can 3 teachers and 4 pupils be arranged in a line if the pupils and teachers must alternate? . how to get the answer? the ans :144
jason
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