Tagged Questions

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

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0
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1answer
764 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
votes
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
vote
1answer
74 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
votes
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 ...
0
votes
0answers
75 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
votes
2answers
157 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 ...
-1
votes
1answer
133 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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2answers
578 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
94 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 ...
0
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4answers
299 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
350 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
4k 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
votes
4answers
2k 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 $n=n_1+n_2+\dots+n_r$ ...
1
vote
3answers
203 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
404 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
votes
2answers
3k 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
votes
2answers
174 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
255 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.
0
votes
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
vote
1answer
102 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
275 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 ...
-4
votes
2answers
1k 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
votes
1answer
299 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
votes
2answers
317 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
votes
2answers
598 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 ...
1
vote
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 ...
1
vote
3answers
84 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
583 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
88 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
64 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
votes
0answers
113 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
votes
1answer
617 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
329 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
votes
1answer
812 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 ...
2
votes
1answer
363 views

Number of permutations with a single fixed point

I know that the number of permutations with no fixed points over a set with $n$ elements approaches $\frac{n!}e$ as $n$ grows. I'm interested in finding a limit (if there's exist) for the number of ...
3
votes
3answers
247 views

Which Digit-Permutations Preserve Divisibility?

This is a completely random question that just happened to come to mind recently and I was wondering if the MathSE community had anything to say about it. Let $n > 1,b > 1$ be integers and ...
1
vote
0answers
264 views

Permutation of N items taken 1,2,3…N at a time.

I want to know the formula for the following: 1.) Permutation of N different items taken 1,2,3...N at a time. 2.) Permutation of N items taken 1,2,3...N at a time but with repeating items. I ...
0
votes
2answers
125 views

How can I figure out every permutation of sets of groups of four students in a class?

I'm trying to develop a grouping system that takes in a bunch of data for when particular students are available to meet and then spits out the "best" groups based on that data. Here I am defining ...
4
votes
2answers
200 views

List of non-immediately-repeating permutations

Background: I am trying to design a scientific trial (computer science dissertation) in which participants will answer 8 questions. There are in fact only 4 questions but each is asked in two ...
3
votes
1answer
345 views

Cards Swapping Problem

The 100 integers from 1 to 100 are each written onto 100 index cards, which are then thoroughly shuffled. To put the cards back into their natural ordering, the only operation allowed is for a pair of ...
8
votes
2answers
124 views

Four generators of $S(9)$ - A smart way of showing that this generates the entire group?

I have four 4-cycles, given by: $(1452),(2563),(4785),(5896)$. I know that the group generated by these guys are $S(9)$ by asking mathematica for the order of the permutation group generated by these ...
9
votes
3answers
543 views

Proof that no permutation can be expressed both as the product of an even number of transpositions and as a product of an odd number of transpositions

I am aware that there are a couple of well-known proofs of this theorem, but I'm specifically grappling with the proof given in Fraleigh's A First Course in Abstract Algebra (Theorem 9.15 in the ...
1
vote
1answer
734 views

How many PINs can you make with x digits?

You want to access a particular smartphone which has a 4-digit numeric pin, entered by tapping the screen. One day you see the owner wipe the screen, unlock the device, and then get distracted and ...
1
vote
3answers
394 views

On permutations of left cosets

Let $K$ be a subgroup of some group $H$; let $X$ be the set of left cosets of $K$, i.e. $X = \{hK: h \in H\}$; and let $G$ be the group of permutations of $X$. For all $h \in H$, let $f\,(h) \in G$ ...
3
votes
2answers
237 views

Existence of subgroup of order six in $A_4$

Show that the alternating group $A_4$ of all even permutations of $S_4$ does not contain a subgroup of order $6$. For me am thinking to write all elements of $A_4$ and trying to find every ...
0
votes
2answers
105 views

How to find the elements of $S_n$?

Consider $S_n$, I do not understand how to get the elements of $S_n$ especially for $n \geq 4$ Any one to show me how simply I can find them. Thanks a lot
1
vote
1answer
142 views

$n$ identical oranges to $k$ identical kids [duplicate]

Possible Duplicate: What is the expression for putting $n$ indistinguishable balls into $k$ indistinguishable cells? I think that this is quite basic, but I can't seem to get it: Given ...
3
votes
2answers
215 views

Is $S_n$ generated by a maximum of n-2 transpositions?

Let $S_n$ be the group of all permutations of the set {$1, 2, \dots,n$}. The question is whether $S_n$ is generated by a maximum of $n-2$ of its transpositions or not. Definitions: A permutation of ...
5
votes
1answer
887 views

A Proof of Correctness of Durstenfeld's Random Permutation Algorithm

Question: Does anyone have a precise mathematical proof of Durstenfeld's Algorithm? The first $O(n)$ shuffle or random permutation generator was published by Richard Durstenfeld in 1964. This ...
4
votes
1answer
334 views

Mistake in a study book?

Here is the exercise from a Pinter's "A book of abstract algebra" from a chapter dealing with permutations on a finite set: Let $\alpha$ and $\beta$ be cycles, not neccessarily disjoint. Prove ...