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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Burnside's Lemma implementation

Can someone please explain to me what Burnside's Lemma theory is about, how to understand if a situation or problem calls for the use this theory? I went through the wiki page but could not grasp the concept. I found it too complicated. Can someone…
riz
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problems on permutation

There are 10 men and 7 women working as supervisors in a company. The company has recently decided to form a committee to represent all the employees. The committee has to consist of 3 members, all of whom must be supervisors. The members will be…
Ishrak Alaxander Hasin
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Sigma of Permutations

Given a permutation p of numbers 1, 2, ..., n. Let's define $f(p)$ as the following sum: $$\large f(p)=\sum_{i=1}^n\sum_{j=i}^n\min({\rm p}_i,{\rm p}_{i+1},...,{\rm p}_j)$$ What is the exact job of this sigma I can't understand it, what is the…
Daniel.V
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Permutations - n people and n seats

Actually, it seams pretty simple, but I just can't figure it out. Imagine we have a room containing $n$ seats in a row and $n$ people waiting in front of the room. The first person that enters the room can decide where he wants to sit. The…
tradt
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Permutations and combinations - distributing objects into groups

Question: In how many ways can $2n$ people be divided into $n$ pairs? Approach: Well as there are $2n$ people, it is obvious that we need to chose each and everyone of them. Using simple counting, the way to divided $2n$ people into $n$ groups is…
Gummy bears
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Why does in a permutation indices move opposite to positions

This is a small notational observation I first noticed when learning about permutations. I am embarassed to admit that I still do not have a satisfactory explanation for it. An example of the phenomenon: Consider a permutation on the ordered set…
past_his_bedtimeman
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How many 2m-permutations, consisting only of cycles of even length?

How many 2m-permutations, consisting only of cycles of even length? I have found this formula: $$Q_2(n) =((2n − 1)!!)^2$$ but how it can be proven?
dehasi
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Find the number of 3 letter words that can be formed from the word 'SERIES'.

To find the number of three letter words that can be formed from the word 'SERIES', with or without meaning and without repetition. The number of permutations if all letters were distinct = $^{6}P_3$. As 'S' and 'E' are repeating, the…
TESLA____
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permutation (retrictions on arrangements) numbers

a list of questions :D 1) how many four digit numbers are divisible by 5 if no two digits are the same? My solution: 9*8*7*2=1008 2)From the digits 0,1,3,5,7,9 how many four digit numbers divisible by 5 can be written if no digit is repreated? My…
Chun Jeff
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Combination of $4$ digit numbers not divisible by $5$

The number of $4$ digit numbers which are not divisible by $5$ that can be formed using the digits $(0,2,4,5)$ if digits are not repeated is?
Vikas
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Permutation elections

During a local campaign eight republician and five democratic candidates are nominated for president. a) If president to be one of thias candidates, how many possibilities are there for the eventual winner? b) How many possibilities exist for a pair…
İsmail Samir USTA
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How to assign values to letters to create unique values per word when all letters are added together?

I'm writing a program to match anagrams in order to practice coding. One way I want to try this is to assign values to letters such that adding up the letters in the individual words creates a unique value. This will allow me to match words without…
texrer
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Using permutations to determine whether given arrangements of the "eight puzzle" are possible.

The "eight puzzle" is a reduced 3x3 version of the 4x4 "fifteen puzzle", which is a very simple game which involves sliding 15 numbered tiles around 16 places, with one free space always being available with each move. The Wikipedia article contains…
Jake
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Why $(12)=(12)(12)(12)∈S_3$ is not a counter example to given claim.

I was assigned the following homework problem over break: Let $g \in S_n$. Show that $g$ can be written as a product of at most $n − 1$ transpositions. Please do not respond with a proof for this claim, as I would really like to construct it for…
Anonymous
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The sign of a given permutation

If I have a permutation $\sigma$ on the set $A$ written by disjoint cycles. There are $n$ disjoint cycles can I then write the sign of the permutation as: $\operatorname{sign}(\sigma) = (-1)^{|A|-n}$?
user145
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