# Questions tagged [permutations]

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

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### Number of angarams of BORBOTTIO in which same letters are close together

I had the following problem: We have the word BORBOTTIO. Find: All the anagrams All the anagrams that starts with BB All the anagrams where the same letters are close together. The first two ...
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### If you shuffle a deck of cards and then someone then shuffles it again is the deck more shuffled?

So we are having a discussion with my friends. One is saying that if he shuffles a deck of cards x amount of times and then somebody else shuffles it again, the deck after the second shuffle is more ...
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### cycle type of product of permutations.

Let $\sigma$ and $\tau$ be two permutations in $S_n$ with partitions $\lambda$ and $\mu$ as their cycle type. What is the cycle type of the product $\sigma \tau$ in terms of $\lambda$ and $\mu$? ...
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### Find the centralizer of $(123)$ in $S_6$.

Find the centralizer of $(123)$ in $S_6$. Is there any software to calculate $C_{(123)}$ where $C_{(123)}$ denotes centralizer of $(123)$ in $S_6$. Can anyone say how to write the code to find ...
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### Finding permutations using the general theorem on inclusion & exclusion

Count the number of permutations $x_1, x_2, ..., x_{2n}$ of the integers $1$ to $2n$ such that $$x_i + x_{(i+1)} ≠ 2n + 1 \quad \text{for all i = 1, 2, ..., 2n-1.}$$ I know I need to use the PIE, ...
Let $H \leq S_N$ be a transitive permutation group. A system of blocks $\Sigma = \{\Delta\}$ for $H$ is a partition of $[N]$ such that either $\Delta^h = \Delta$ or $\Delta \cap \Delta^h = \emptyset$. ...
I tried this way: Taking 'UE' together and remaining 'PZZL'. So, as 'Z' is repeating, I divide it by $2!$. My answer: $(5!/2!)\cdot 2! = 120$. Is it right? And why do we divide by its factorial if ...