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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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90 degrees CCW permutation of a square ($D_4$)

Given a square and a permutation of 90 degrees counter-clockwise, what is the order of this finite symmetry group? Here's an attempt: $$\rho =\begin{bmatrix} 1 &2 &3 &4 \\ \rho (1) &\rho(2) &\rho(3) &\rho(4) \end{bmatrix}=\begin{bmatrix} 1 &2 …
opensource.11
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Is it possible to develop function that returns the number (rank, position) of a particular permutation.

I'm working on a data warehousing project and need to assign a unique value to a permutation and store that value as dimension in the data warehouse. Currently, I'm relying upon a rather large lookup table to determine the unique value and I'm…
Mutuelinvestor
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A problem on permutation

Question :If there are $6$ periods in each working day of a school,in how many can one arrange $5$ subjects such that each subject is allowed at least one period? My solution: ${^5P_5} *{^5P_1}=600$ Logic that I used is:out of 6 periods,5 periods…
user237454
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Determine the numbers of permutations $\sigma$ so $\gamma '= \sigma \gamma \sigma ^{-1}$

I have a question regarding permutations. If $\gamma = (123) (45) (6)$ and $\gamma ' = (1)(23) (456)$ in $S_{6}$ how do I then determine the numbers of permutations $\sigma$ in $S_{6}$ so $\gamma ' = \sigma \gamma \sigma ^{-1}$? How do I do this…
bemyguest
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permutations with specified repetition counts

Problem: Determine the number of permutations of the characters for: AABBBC How can I calculate a problem like this generally, given a set of characters and a number of times each has to appear?
golom889
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For a given set of pairings in the 8-team basketball tournament,in how many ways can the top 3 positions in the final standings be filled?

The top 2 teams must be from different brackets. I couldn't understand the question.In the initial competition,8 teams are separated into 4 groups(with 2 teams each) to compete.And it will give 4 winner teams.But how can we choose the top 3 from 4?
JimfyWinsy
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how to find the number of different arrangements when a coin is thrown 12 times and gets 5 heads

Suppose a fair coin which has 2 faces-Head(H) and Tail(T) is thrown 12 times and we get exactly 5 heads: $$H,H,H,H,H,T,T,T,T,T,T,T$$ How can I find the number of different arrangements it can have? One possible…
Irtiza
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How many permutations of $x^5 + y^5 + z^5$ are possible given x, y, z are integers such that $1 \le x \le y \le z \le 180$?

I initially thought it would be $180^3$ possible permutations, but then quickly realized that something like $x=3, y=2, z=1$ would not be valid due to the constraints. How can I go about trying to figure out how to solve this?
user3261567
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Permutations and Combinations 2

The word ARGENTINA include the four consonants R,G,N,T and the vowels A,E,I How many of the arrangements have a consonant at the beginning,then a vowel,then another consonant at the beginning,then a vowel,then another consonant,and so on…
Irtiza
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$a_n=a_0a_{n-1} + a_1a_{n-2} \dots + a_{n-1}a_0$

let σ∈Sn and τ∈Sm with m$\leq$n . We say σ avoid the permutation τ if there are no subset ${j_i< \dots
Noah
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How to find the rank of linear permutation when replacement is allowed?

Question: If all $5*5*5*5*5*5*5*5=5^8=390625$ 8-digit numbers obtained by arranging (permuting) the five digits $2, 3, 6, 7$ & $9$ with their replacements are arranged in the correct increasing order as…
Harish Chandra Rajpoot
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If $m$ and $n$ women are standing toghter ]such that no men are woman are adjacent together what are the number of Permutations

suppose $m$ men and $n$ women from a single line in such a way that no two men are next to each other and no women are next to each other how many lineup are possible ? Never solved these problems before with $m$ and $n$
Connor Verlekar
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Let $f \in 8^8$ where the permutation is given in two line form:

I'm having trouble understanding how one would answer question's like this. $$\begin{pmatrix} 1&2&3&4&5&6&7&8\\ 3&4&5&8&1&2&7&6\end{pmatrix}$$ Find $f^{80}(1)$ and $f^{80}(2)$ Could someone please explain how to go about solving problems similar to…
Socrox
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To find number of questions when number of wrong answers is given

In a certain test there are n questions, in this test $2^{n−i}$ students gave wrong answer to at least i questions where i=1,2,3,…,n. If the total number of wrong answers given is 2047,what is the value of n? My attempt:From the question $2^{n−1}$…
GrandAlpha
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Figure Out Possible Combinations

I am trying to figure out how many possible of combinations I can have between two sets of values. My two sets looks like this: Set 1: [White, Black] Set 2: [Blue, BlueGreen, Brown, Orange, Pink, Purple, Red, Yellow, YellowGreen] Set 1 has two…
user6673
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