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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Permutation of an element

An array $\mathbb T$ has elements $T_{ijkl}$ where $i,j,k,l=1,2,3,4$. It is given that $$T_{ijkl}=T_{jikl}=T_{ijlk}=-T_{klij}$$ for all values of $i,j,k,l$. The number of independent components in this array is I don't know how to solve this…
Harshit Tiwari
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Finding all permutations which permute with a certain one

I have found this topic here: How to find all the permutations which commute with a certain one, but I still could not understand it. Could anyone please explain how to think about doing it? If I have (12)(34), working in the symmetric group 4 for…
Valentin
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Number of permutations of n distinct objects when a particular object is always included in any arranegement

In this theorem I understand that if there are n objects and r number of objects are taken at a time and if any one object is always included in any arrangement then what we do is ($n-1!/r-1!$)-(i) but why in the formula are we multiplying (i) by r?…
Mad Dawg
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Repeated alphabet in n^r

Q: How many ways to form a word of 3 letters with English alphabet (repetition allowed)? A: 26^3 but shouldn't we account for the repeated alphabet? like aab, and aab is the same? Why isn't the question solved in the same way like "How many ways to…
thi
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Question about permutation?

Can someone help me with this permutation exercises... 1) In a NY parade, there are 8 floats and 3 orchestras. How many possible orders are there? Ok. Tell me if I'm right. There is no repetition in here. So if I'm going to line them up this will be…
bdvg2302
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Number of ways to arrange 0 marbles?

A game has to be made from marbles of n colors, where n marbles has to be kept one upon another. In how many ways these marbles can be arranged? Is the answer is $1$ if $n = 0?$
Mohamed Magdy
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Write a permutation as a product of transpositions.

Let $\alpha = (1 \ 6 \ 3) (2 \ 9) (4 \ 8 \ 10) \in S_{10}$ be a permutation. Write $\alpha$ as a product of transpositions, i.e. of cyclic permutations of order 2. Note that transpositions do not need to be disjunked. Really don't know how to…
soetirl13
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Calculate two permutations

Let $\alpha = (1 6 2) (4 5)$ and $\beta = (1 2 3 6)$ be permutations in $S_ {6}$. Calculate the product $\beta \alpha$. Answer with a product of disjunked cycles. I don't know how to do it, but maybe something like this; Step 1: I think that if we…
soetirl13
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Even permutations, what is wrong?

Watch this following permutation in $S_8$ choose the even one's. A. (1 5 2 8 3 6) B. (1 5 4)(2 6) C. (3 8)(4 7 6) D. (1 8 4)(3 7 5 6) E. (1 8 5 4 6 3 2) F. (1 7)(3 4 5)(6 8) even*even = even even*odd = odd odd*odd=even in their…
soetirl13
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Counting number of friendly triplets

A triplet (a,b,c) is called friendly if product of any two is equal to third number . Find number of such ordered triplet. a,b,c are real numbers
maveric
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Permutations from 1 to 10, starting always with 1 and with a step not bigger than 6

I would appreciate your help on the following: I need all permutations from 1 to 10, starting always with 1 and with a step not bigger than 6. Thank you very much in advance!
Dimitrios
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In how many 4th permutations of given subset $a$ and $b$ are adjacent?

Suppose we are given that $$K = \{a,b,c,d,e,f\}$$ In how many 4th permutations of given subset $a$ and $b$ are adjacent? So we have four choices for remaining letters when we put $a$ and $b$ $$ab\_\space \_$$ Now let us pick 2 letters out of 4…
Fiv
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Finding maximum ways to separate

Lets say I have a group a students. I am to put them into rooms, and each room must contain at least 5 students. The number of rooms can be varied, and I am to find the number of ways to do so. Question: how many ways are there to separate 100…
Electricboy
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In how many different ways three persons A, B, C having 6, 7 and 8 one rupee coins

In how many different ways three persons A, B, C having 6, 7 and 8 one rupee coins respectively can donate Rs.10 collectively
juantheron
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What will be the percentage of plants with red and white flowers in the final population?

Well,I'm supposed to find out the number of pink flowers to the red flowers and I started 'manually' selfing the generations. This seemed to manually impossible and so one colleague suggested I use nPr and nCr to solve it.I have the basic idea of…
Koushal
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