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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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There are 10 speakers in a conference $S_1, S_2..S_{10}$ and $S_1$ speaks only after $S_2$ has spoken...

There are 10 speakers in a conference $S_1, S_2..S_{10}$ and $S_1$ speaks only after $S_2$ has spoken, then find number of ways in which speakers speak. Using string method, let $S_1$ and $S_2$ be one block. Also there is only one way to arrange…
Aditya
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How do I permute a list of integers so that as many possible integers will move to a place where a smaller integer used to stand?

I'm trying to understand the solution to an algorithm/logic problem. The problem statement is as follows: You are given an array of integers. Vasya can permute (change order) its integers. He wants to do it so that as many as possible integers will…
discovery
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Complexity of describing a permutation

Please forgive me if my terminology is lacking. I have been thinking about permutations and it occurs to me that some permutations are very easy to describe, while other are much more difficult. For a set $\{0,1,...,N-1\}$ there are $N!$ possible…
Chris_F
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Ordering of elements

I have 40 elements I need to order (for simplicity just call them "1" - "40"). There are a few rules regarding how I must order some elements: Elements "2" and "5" must go before element "10", Element "10" must go before element "7", Element "7"…
user882441
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Confusion regarding Permutation as disjoint cycles

The question is to write the permutation $(123)(16543)$ as disjoint cycles. First attempt (The wrong one): $(16543)=\begin{pmatrix} 1 & 2 &3 & 4& 5&6\\ 6&2&1&3&4&5 \end{pmatrix}$ $(123)=\begin{pmatrix} 1 & 2 &3 & 4& 5&6\\ 2&3&1&4&5&6 …
Oualid
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Work team sitting at a table question

A question came up recently: There is a team sitting at a round table. They all leave the table for a lunch break, and after returning to the table, each person finds that both their neighbours on the right and on the left do not sit next to them…
Leo
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Computing $N_{S_n}(S_m)$ with $m

Let $m
eraldcoil
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number of permutations in which all number changes

What is the number of permutations in which all number change position? For example, suppose a ordered set (12345678...n) What is the number of permutations this (below) is not allowed: Let P be, let's say, the permutation operator, and a_{i} the…
Lac
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Permutation with Grouped Objects and Repetitions

I have letters AAABCD. The letters A and B must be together. How many ways can I arrange these 6 letters? At first, I thought the answer would be to group one of the A's and B together, and treat it as one object, so that's 5! ways of arranging…
Chung Ren Khoo
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Permutation Question - digital images

First, I am not a math specialist, I am asking a question that seems to have a very clear answer to me but it seems wrong, so I am hoping to learn why. Here goes... Long ago I read a description of Maxwell's Demon in a Douglas Hofstadter book (I…
Steve Valliere
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Finding number of permutation of a word given conditions

Find the number of permutations of the word "ATTITUDE" such that no two "T" occur together Using inclusion exclusion principle only. I found the total number of permutations which is $8!/3!$ then i took both T as a unit "a" thus the number of…
Math enthusiast
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Find the Distinct Variants of $\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_2-x_3\right)$

I want to know if there is a way to find the distinct variants of a function such as $\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_2-x_3\right)$ more efficiently than just writing out and tabulating every permutation of the variables. My…
Chairman Meow
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Let f ∈ S3 be a permutation which is not the identity. Prove that there exists g ∈ S3 such that fg ≠ gf.

Question: Let f ∈ S3 be a permutation which is not the identity. Prove that there exists g ∈ S3 such that fg ≠ gf. My attempt: First list out all the possible permutations of f (which there are 5 of them as it is not identity); then list out all…
sasaki085
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How to prove fg doesn't equal to gf in permutation?

1.Let f ∈ S3 be a permutation which is not the identity. Prove that there exists g ∈ S3 such that fg ≠ gf. 2.Let n ≥ 3, and let f ∈ Sn be a permutation which is not the identity. Prove that there exists g ∈ Sn such that fg ≠ gf. Hey guys I am…
sasaki085
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