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

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2
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1answer
398 views

Combinatoric puzzle

During a dinner with $k=20$ persons sitting at $n=4$ tables with $m=5$ seats, everyone wants to share a table with everyone. The assembly decides to switch seats after each serving towards this goal. ...
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2answers
174 views

Find number of possible arrangements of N disks with given constraint

In how many ways you can make a stack of N disks, such that: Bottom disk always has radius 1 A disk can be placed on the stack if it radius is <= (maximum of all disk radii below it + 1) You ...
3
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3answers
680 views

What is the correct terminology for Permutation & Combination formulae that allow repeating elements.

Let me explain by example. Q: Given four possible values, {1,2,3,4}, how many 2 value permutations are there ? A: 16. ...
0
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2answers
54 views

Jacobi symbol and invertibility of $m$ for an odd $n$

I have asked a similar question here before, and received a nice answer. I think that the next question here is equivalent, but can't seem to be able to prove it. Here goes: Given an odd $n$, I want ...
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0answers
108 views

How many ways to fill the $N \times N$ board by nonnegative integers, such that sum of the numbers of each row and each column is $R$?

How many ways to fill the $4 \times 4$ board by nonnegative integers, such that sum of the numbers of each row and each column is $3$? I wrote a brute-force and got $2008$ which seems to be the ...
0
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2answers
190 views

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 ...
3
votes
1answer
569 views

Permutation questions

What is the smallest number n such that $A_{n}$ contains a permutation of order 2004? I calculated it to 334, but the answer is 176 and I can't see why? I first noticed that $2004 = 2^{2}\cdot 3 ...
1
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1answer
59 views

Permutation of order 12 and 30 in $S_{9}$

If I have the group $S_{9}$ and $\sigma, \tau \in S_{9}$ where $\vert \sigma \vert = 5$ and $\vert \tau \vert = 6$ is it then possible to have $\vert \sigma \tau \vert = 30$ and $\vert \sigma \tau ...
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2answers
520 views

How many seven-digit numbers satisfy the following conditions?

How many seven-digit numbers divisible by 11 have the sum of their digits equal to 59? I am able to get the seven-digit numbers divisible by 11 and I am also able to get the seven-digit numbers ...
5
votes
1answer
102 views

Is there a “natural” transitive action of $SL_2(\mathbb{F}_5)$ on a set with 5 elements?

I'm really looking for a "cute" way of showing that $SL_2(\mathbb{F}_5)$ is a double cover of $A_5$. The sort of action I am looking for is something like the action of $GL_2(\mathbb{F}_3)$ on ...
0
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1answer
129 views

Is the permutation $\alpha : \mathbb Z_{11} \rightarrow \mathbb Z_{11}$ given by $\alpha(x)=4x^2-3x^7$ a cycle or not?

The permutation $\alpha : \mathbb Z_{11} \rightarrow \mathbb Z_{11}$ given by $\alpha(x)=4x^2-3x^7$ is a cycle? If it´s not a cycle then write it as a product of disjoint cycles. I have already ...
1
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1answer
313 views

Combinatorics, arrangements (edited)

"How many ways can the letters in the word SLUMGULLION be arranged so that the three L’s precede all the other consonants?" My work is below: Can someone also solve this ONLY using the multiplication ...
1
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1answer
111 views

Permutations in $A_n$ within a proof of simplicity

Some time ago I wrote a message about a proof for the simplicity of $A_n$ in the case $n \geq 5$, taken form Bhattacharya's book. After some time I read that proof again and found something that I ...
0
votes
1answer
405 views

What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?

What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters? I believe the answer for this is 6. As we can write the group elements as below (a)(b)(C) (ab)(c) ...
2
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3answers
1k views

Keeping track of how to calculate probability/permutations/combinations?

I'm absolutely terrible at calculating these things and I would like to, especially with SATs coming up, improve my capabilities. What always gets me is that there are so many types of ways to ...
3
votes
3answers
3k views

What is the inverse cycle of permutation ?

Given a cycle in of a permutation , for example : $σ=(123) $; $σ_{2}=(45)$ What is the inverse cycle ? meaning $σ^{-1}$ Regards
0
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1answer
677 views

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, ...
0
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1answer
64 views

How many homomorphims from $Z_{12}$ to $S_{5}$

I'm trying to calculate how many homomorphisms exists from $Z_{12}$ $\longrightarrow$ $S_{5}$ . Here are the options : $(x x x x x)$ order 5 $(xxxx)$ order 4 $(xx) (xx) $ order 2 ??? $(xxx)(xx) ...
1
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1answer
72 views

Encoding of a combination

If you have a set of $n$ integers ranging from $1$ to $n$ and you need to pick (create a tuple with length) $\sqrt{n}$ ($n$ is a valid square). One could encode that with an integer ranging from $1$ ...
2
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1answer
1k views

Permutations and Combinations - How many different ways to do certain things before having to repeat?

Recently, while reading, I came across a problem in Problem Solving Strategies: Crossing the River with Dogs by Ken Johnson and Ted Herr that I was not entirely sure how to solve. Alas, I have come ...
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0answers
74 views

Calculate pairing in a rotational system

I'm not even sure how to word this question. So I'll explain it out. I've got these values: A1, A2, B1, B2, B3, C1, C2, I need each A to be paired with each B and C each B with each A and C ...
2
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1answer
112 views

How i can find the sum of the series? $\binom{n}{1} + \binom{n}{2} + \cdots+ \binom{n}{\frac{n - 1}{2}} $

Find the sum of the series when n is equal to 83? $$\binom{n}{1} + \binom{n}{2} + \cdots + \binom{n}{\frac{n - 1}{2}} $$ I have got some idea that the trick to solve this particular problem is by ...
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1answer
132 views

What do you call a permutation that is no where identity?

I want to write a formula for $n!$. $n!$ is the number of permutation functions on the set $\{1,\ldots,n\}$. Let's define a "true k-permutation" on $\{1,\ldots,n\}$ as a permutation that is identity ...
21
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3answers
543 views

Permutations with restriction

We have $n$ types of objects, and the number of objects of type $i$ is $a_i$, $1\leq i\leq n$. What is the number of permutation of the $\sum_{i=1}^n a_i$ objects, if no two objects of the same type ...
2
votes
1answer
91 views

Question about permutations in $A_n$

A proof that $A_n$ is simple ($n>4$) begins as follows: Suppose $H$ is a nontrivial normal subgroup of $A_n$. We first prove that $H$ must contain a $3$-cycle. Let $\sigma \neq e$ a permutation that ...
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4answers
281 views

How many permutations?

I'm trying to calculate the number of possible non-repeated permutations of these serial key styles. I have no mathematical background and cannot read formulas, which is why I'm struggling with ...
0
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3answers
272 views

Number of ways in which $38808$ can be expressed as a product of 2 coprime factors?

Number of ways in which $38808$ can be expressed as a product of $2$ coprime factors ? the answer given is $8$ ways, what I did was, $$38808 = 2^3 \times 3^2 \times 7^2 \times 11$$ so the number ...
0
votes
4answers
3k views

How many ways can four letters abcd be arranged such that a always comes before b and c always comes before d?

How many ways can four letters abcd be arranged such that a always comes before b and c always comes before d? Total number of ways abcd can be arranged? 4! Half of them a if before b, half b is ...
2
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4answers
1k views

What is the proof of permutations of similar objects?

What is the proof of permutations of similar objects? I know the formula, but I cannot figure out how to derive it! permutations of similar objects The number of permutations of $n=n_1+n_2+\dots+n_r$ ...
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3answers
200 views

Conjugacy classes — how to generate them for a list to be sorted?

In another thread I had brought up the notion of sorting a list of four randomly scrambled items. It was mentioned that they can be broken down into 5 conjugacy classes: (), (12), (123), (12)(34) and ...
2
votes
2answers
371 views

How many ways can $n$ adults, $k_1$ boys and $k_2$ girls be seated in a line such that no two children of the same sex sit next to each other?

It was shown in this question that the number of ways $n$ adults and $k$ children can be seated in a line such that no two children are sitting next to each other is: $$\binom{n+1}{k}n!k!.$$ Now ...
9
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2answers
2k views

Given 5 children and 8 adults, how many ways can they be seated so that there are no two children sitting next to each other. [duplicate]

Possible Duplicate: How many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other? Given 5 children and 8 adults, how many different ways ...
0
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2answers
171 views

Selecting $P$ actors from $N$ boys and $M$ girls, with at least 4 boys and 1 girl [duplicate]

Possible Duplicate: Combinatorics-N boys and M girls are learning acting skills from a theatre in Mumbai. N boys and M girls are learning acting skills from a theatre. To perform a play ...
4
votes
1answer
228 views

How many permutations of $\{1,2,…n\}$ derange the odd numbers?

How many permutations of $\{1,2, \dots , n\}$ derange the odd numbers? I have the answer in my text book but I don't know how they got it.
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2answers
2k views

some questions about combinations

1) In how many ways can 10 pencils (identical) be distributed among 5 children if a) there are no restrictions? b) each child gets at least 1 pencil? c) the oldest child gets at least 2 ...
1
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1answer
101 views

pseudo-random permutation of $[0,N)$

Given a positive integer: $$\begin{align*} N \in \mathbb{Z}^+ \end{align*}$$ I would like a function: $$\begin{align*} f : \mathbb{Z}^2 \rightarrow \mathbb{Z} \end{align*}$$ such that ...
2
votes
1answer
255 views

Algorithm to find a permutation that contains the fewest possible monotone subsequences of length $k$

Fix natural numbers $k,n$, with $k<n$. I want to find a permutation in $S_n$ that contains fewest monotone (increasing or decreasing) subsequences of length $k$. For example the permutation ...
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votes
2answers
952 views

How many ways can we order a set of $n$ elements?

If you have $n$ CDs to arrange sequentially on a shelf, say for $1 \le n \le 20$, how many ways can they be ordered? Please also explain the solution steps.
0
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1answer
261 views

k-cycles and permutations

I'm trying to understand a proof from Yahoo Answers http://in.answers.yahoo.com/question/index;_ylt=ArPgiZQnQIXqbb0t61DlLusazKIX;_ylv=3?qid=20120209041852AANkOYp It does not look like part (a) is ...
4
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2answers
290 views

Confused about permutation cycles - Question on joint cycles of odd length

For some reason I'm finding permutation cycles to be strange and hard to deal with. Let $\alpha$ and $\beta$ be cycles of odd length (not disjoint). Prove that if $\alpha^2 = \beta^2$, then ...
6
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2answers
521 views

How many ways are there for people to queue?

I'm stuck at the following combinatorics problem: Fifteen people queue up for cinema tickets at five (different) sales points. In how many ways can they stand in queue behind one another, if the ...
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1answer
1k views

Probability that no two people get off elevator on same floor

Seven people enter the elevator on the first floor of a $12$ story building. What is the probability that no two will get off on the same floor? You may assume that all floors are equally likely and ...
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3answers
81 views

Number of different permutations

Consider some text $T$ How many different permutations of this text can we achieve ? The easiest case is when every letter appears only once in the text, so the answer is $|T|!$ But when we have ...
0
votes
1answer
514 views

How to arranged two or more different colored blocks in all possible ways?

Is any algorythem that can arrange two or more different blocks in all possible ways.. in series (rows and columns.)? If I have two colored(red and blue) blocks and I try to arranged in one possible ...
2
votes
1answer
82 views

Given an permutation $a$ in $S_8$ how to find $a^{14}$?

Given the following exchange in $S_8$: $$a = \left(\begin{array}{cccccccc} 1& 2& 3& 4& 5& 6& 7& 8\\ 2& 5& 8& 3& 1& 7& 6& 4 ...
2
votes
1answer
60 views

What exactly does the relation over the set $X$ mean concerning orbits?

My book says this: Suppose that $G$ is a group of permutations of a set $X$. We shall show that the group structure of $G$ leads naturally to a partition of $X$. Define a relation $\sim$ on ...
0
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0answers
109 views

Closed form some permutations

Is there a closed form expression for the the permutation $\tau$ where $(\tau(1) \tau(2) \ldots \tau(q))=(1 2 \ldots q)^k$ where $q$ is a prime? I have found that for $q=5$, $\tau$ can be expressed as ...
0
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1answer
541 views

How many permutations with this set of rows and columns?

I have a range of possible page design layouts consisting of rows and columns in those rows. There are a maximum of 6 possible rows, and a maximum of 5 possible columns per row. How many unique ...
2
votes
2answers
315 views

Symmetric Group S3 Symmetry

Consider the action of the full symmetric group $S_3$ on the cube $[0,2] \times [0,2] \times [0,2]$. Classify the orbits of this action and determine their cardinalities. My Answer: What I note is ...
0
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1answer
696 views

Solving permutation problem

I need to know the proper way to solve this kind of problem:Five employees of a firm are ranked from 1 to 5 based on their ability to program a computer.Three of these employees are ...