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

learn more… | top users | synonyms (1)

1
vote
2answers
23 views

Question about permutations: How to show $\sigma(P)=(-1)^{\imath(\sigma)}P$?

A permutation of a finite set $X$ is any bijection from $X$ to $X$. We denote by $S(X)$ the set of all permutations of $X$. If $I_n:=\{1, \ldots, n\}$ we write $S_n$ instead of $S(I_n)$. Define ...
1
vote
1answer
17 views

Parity of permutation example

I know the definition of parity of permutation. But what does that look like in examples? For example, if the number of permutations is odd, then the sign of permutation in $-1$. What does this mean? ...
1
vote
2answers
30 views

24 possible combinations?

I'm terrible at math. My goal was to try and create $24$ total combinations using a horizontal bar, and a horizontal bar with one break. So that's two bar types. How can I write out the math that ...
1
vote
1answer
14 views

How many different arrangements of these 7 dogs are there if no poodle is next to another poodle?

Question: 2 Spaniels, 2 retrievers and 3 poodles go through to the final. They are placed in a line. How many different arrangements of these 7 dogs are there if no poodle is next to another poodle?
0
votes
1answer
37 views

Number of possible passwords - Google APAC Test

I am trying to solve this problem - Google apac test - Password Attacker . Problem summary: Using $M$ distinct characters, what is the number of ways of making a password of length $N$, such that ...
0
votes
1answer
19 views

Example of an elementary permutation

Can someone please give an example of an elementary permutation? The book says that every permutation can be written as a composite of elementary permutations. Can someone please give an example? ...
0
votes
0answers
25 views

Count number of trees

Given an array with n elements which is the pre-order traversal of a tree. How many max-heap will have the same pre-order traversal?
3
votes
1answer
64 views

Arrangement of integers in a row such that the sum of every two adjacent numbers is a perfect square.

Inspired by this interesting question and in order to solve an old problem, I have the following question: Can we construct a strictly increasing sequence $(N_i)_{i\in \mathbb{N}}$, such that for ...
0
votes
1answer
39 views

Murder mystery permutation problem

In exploring a hypothetical situation, I ran across this problem and I'm curious to know the answer, but math's not really my forte. You have a pool of 15 people. Between these 15 people there will ...
0
votes
0answers
18 views

Find lexographically minimum permutation with maximum sum

A wavy sequence "a" is a sequence of N integers such that a[0] < a[1] > a[2] < a[3] > a[4] ... and so on. And let say value of this sequence is sum of |a[i] - a[i - 1]| for all 0 < i < N. ...
1
vote
2answers
32 views

How to find the number of strings of length N that can be formed by using the characters A, B, and C only that do not have “ABC” as a substring?

A, B, and C can be used any number of times in the string. This problem appeared in a programming contest which is already over. http://www.codechef.com/problems/CDSW152
1
vote
1answer
22 views

What kind of mathematical approach can you use to find all non-repeated combinations?

At first glance I thought this was a non-repeated combination or permutation, but those use a set length. So, I guessed this might be a partition of a positive integer, but it's not looking like that. ...
4
votes
1answer
33 views

An Example for a Graph with the Quaternion Group as Automorphism Group

I am reading "Graphs of Degree Three with given Abstract Group" (by Robert Frucht) where the author describes (somewhat tedious) algorithms to construct suitable graphs starting from a given group. I ...
2
votes
0answers
14 views

How to calculate total results of combinations of letters

I am programmer and have developed an algorithm to run a processor intensive function on all the permutations of 2 letters (X and O) when we define how many X's and O's there will be. For example, I ...
1
vote
0answers
26 views

Structure of the semidirect product decomposition

I'm looking at a complicated group that involves many semidirect products, and I realized that I have a fundamental confusion about how to use the structure of a semidirect product decomposition of a ...
1
vote
1answer
29 views

Possible permutations of a grid

I hope this is the correct place to post this, as I don’t study maths. But I do need help calculating the possible permutations of a grid based game I’m currently programming. This isn’t to help out ...
0
votes
1answer
35 views

Find Number of combinations possible

There are two letters "X" and "Y".A String of length N needs to be formed using those two letters How many number of combinations that can be possible where N should start with "Y" and no two or more ...
0
votes
0answers
27 views

Number of ways to color N objects in X colors where there is at least one object of each color.

What is the number of way to color $N$ objects in $X$ colors, where there is at least 1 object of each color?
4
votes
1answer
73 views

Combination or Permutation

I am searching for the number of possible isomers of a compound. However, my understanding of mathematics is quite limited in the field of combination and permutation. I have searched through many ...
1
vote
0answers
14 views

Generating uniform permutations by a particular method

Let $A$ be a uniformly random permutation of the numbers $\{1,2,\cdots,n\}$. I want to generate a uniformly random permutation from $A$ on the numbers $\{1,2,\cdots,n,n+1,\cdots,n+m\}$. In other ...
1
vote
1answer
39 views

How many cycles of length $k$ in $S_n$?

In the symmetrical group $S_n$, how many cycles of length $k$ can we form? After some research I am tempted to say $\frac{n!}k$ but I am not sure.
1
vote
2answers
24 views

Dependent permutations, a question.

I cant seem to find anything on the internet on this subject , and the professor did not explain it too well, in short the following is unclear to me how is $$(1 3 4)(236)=(24136)$$and ...
2
votes
1answer
21 views

Symmetries of the regular hexagon

Q- Let G be the group of the symmetries of the regular hexagon. List the elements of G (there are 12 of them), then write the table of G. So for the listing the elements of G, they want it like this: ...
1
vote
0answers
26 views

Integrating a permutation of a combinatorics-type function

I would like to integrate a permutation of a function. Namely I have the following: $\sum_{\sigma, \sigma'\in S_{n+1}}\int_{-A}^A dz_1dz_2 ... dz_{n+1} ...
0
votes
0answers
28 views

Ball-of-wacks combinations

The six-color version of the ball-of-wacks consists of thirty rhomboidal pieces, which can be combined to form a rhombic triacontahedron. There are six colors, each with five pieces. One challenge ...
2
votes
2answers
30 views

Illegal permutations give a nonzero answer

I am told that a random variable can take a value of $+1$ or $-1$. I am given the total number of times the random variable is counted, $N$, and the sum of the random variables, $n$, and asked to find ...
3
votes
1answer
39 views

List the elements of the cyclic subgroup of $S_6$

List the elements of the cyclic subgroup of $S_6$ generated by: \begin{smallmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 2 & 3 & 4 & 1 & 6 & 5 \end{smallmatrix} ...
1
vote
1answer
33 views

How many three digit number can be formed?

Question: (a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (b) How many of these are odd numbers? (c) How many are greater ...
1
vote
0answers
21 views

Birkhof representation of a stochastic matrix

From Birkhof Theorem, it is known that every doubly stochastic matrix can be written as a convex combination of permutation matrices although this representation might not be unique. I have the ...
0
votes
1answer
27 views

no of possible ways [duplicate]

we have to build a houses on $m$ plots, such that no two consecutive plots exist on which it is allowed to build house calculate the number of possible ways of assigning free plots to buildings ...
2
votes
1answer
32 views

The order of a $k$-cycle in $S_n$ is $k$.

Here's what I have right now: The order of a $k$-cycle in $S_n$ is $k$. Proof. Let $\sigma$ represent the $k$-cycle $$\sigma=(x_1 \ x_2 \ \cdots \ x_k)$$with distinct elements $x_i$. Note that the ...
2
votes
1answer
20 views

How to solve this statistics problem? [closed]

Can you find the sum of all numbers that can be formed with the digits $2, 3, 4$ and $5$ taken all at a time? (So its like you sum up the number from 1st digit to 4th digit) I'm learning now about ...
0
votes
2answers
22 views

Permutation's decomposition into transpositions

Transposition is a cycle with 2 elements. Any permutation can be decomposed into a product of transpositions. For example, for permutation $\begin{pmatrix} 1 & 2 & 3 & 4\\ 2 & 3 ...
2
votes
1answer
42 views

Maximize $a_1^{a_2^{\ldots^{a_n}}}$, where $(a_1,a_2,\ldots,a_n)$ is a permutation of $(b_1,b_2,\ldots,b_n)$

You are given a tuple of integers $B=(b_1,b_2,\ldots,b_n)$. Find $(a_1,a_2,\ldots,a_n)$ - a permutation of $(b_1,b_2,\ldots,b_n)$ - that maximizes $a_1^{a_2^{\ldots^{a_n}}}$. For example - If ...
0
votes
0answers
42 views

Permutations Without Repetitions

Given the set [A,B,C,D] how many distinct ways can I order all four of the members of the set? I see distinct, as a unique set, therefore [A,B,C,D] and [D,C,B,A] ...
0
votes
1answer
31 views

How to calculate combinations of multiple variables which can assume multiple values

I have 3 variables (A,B,C); each variable can assume 3 different values (1,2,3) . I want to calculate ho many combinations there are which follow this rule: let's fix A1, then cycle on all the others ...
3
votes
3answers
233 views

How many ways to reach a given tennis-score?

Let's say a tennis player wins a set with a game score of 6-3. In how many different ways can we reach this score? Assuming H means the home-player won the game and A means the away-player won the ...
4
votes
2answers
70 views

Number of Words with two letters $a$ and $b$.

Given $N$ and $M$, find the number of $N$ letter words consisting of only $a$ or $b$, where $b$ must not be consecutive for more than or equal to $M$ times. Example: if $N=3$ and $M=2$, then all the ...
0
votes
1answer
21 views

Combinations - Permutations

Find the number of ways in which 5 books can be distributed between three people A,B and C, if the books are a)indistinguishable, b)all different. a) $\displaystyle \frac{5!}{3!(5-3)!} = 10$ b)$ ...
3
votes
1answer
200 views

Counting elements in cartesian power with plurality + pattern constraints

Problem: I have an alphabet with n=8 letters (say $X=\{A, B, C, D, E, F, G, H\}$). I'm looking for words with m=24 letters, with three constraints: letter $A$ is the relative majority (like in ...
-1
votes
1answer
26 views

symmetric group acting on torus

Let $S_k$ be symmetric group of order $k$. Let $T^k=S^1\times\cdots \times S^1$. Then $T^k$ is a Lie group. For each $\sigma\in S_k$, let $\sigma$ act on $T^k$ from right in the way $$ ...
4
votes
2answers
55 views

If there is a bijection $f: X\rightarrow Y$, prove that there exists an isomorphism $\phi :S_X\rightarrow S_Y$

If there is a bijection $f: X\rightarrow Y$, prove that there exists an isomorphism $\phi :S_X\rightarrow S_Y$. Here $S_X$ denotes the group of all permutations of $X$, i.e., the bijections $X\to ...
0
votes
1answer
28 views

Permutations and Counting problem?

Postal codes in Canada have six characters with alternating letters and digits in the form L#L#L#. How many postal codes do not have one letter repeated three times? What I did is ...
0
votes
0answers
20 views

Sampling with/without order

Our professor have presented this simple example in the lecture. You have $P_n$ processors and $M_k$ memory where $k>n$. If two or more requests goes to same memory then the request will be ...
0
votes
1answer
36 views

Sides of a triangle [closed]

The sides of a triangle are $a,b,c$ and $a\leq b\leq c$ If $c$ is given, show that number of different triangles is $(c+1)^2/4$ or $c(c+2)/4$ according to $c$ is odd or even. Also given a,b,c are ...
2
votes
0answers
35 views

The $8$-Puzzle and $2$-Cycles

I have been studying the $8$-puzzle and have thus far managed to wrap my head around the following information: The following illustrates the solved position of the $8$-puzzle, where $9$ is the empty ...
0
votes
1answer
49 views

Prove that this number is an integer

Prove that the number $${4155 \cdot4156 \cdot\ldots \cdot4251 \over 2 \cdot3 \cdot\ldots \cdot 97}$$ is an integer. How might I prove this?
0
votes
1answer
42 views

Adding numbers in a consecutive series

I have the series: 1, 13, 133, 1333 ... Currently I have distributed it down to: 1 + (10 * 2) + (100 * 2) ... Can anyone point me in the right direction? Sorry, I forgot to mention, I'm looking for ...
0
votes
1answer
33 views

How many permutations of letters ABCDEFG contain the strings ABC and CDE

For this problem, I understand how to find something like how many strings contain the string BA and GF. I just look at the set of letters like this: {BA, GF, C, D, E} and since I have 5 distinct ...
0
votes
2answers
14 views

Counting permutations of a set that doesn't fix elements

I want to know how to count the number of permutations of a finite set that doesn't fix elements, i.e., the cardinality of the set $H=\{f\in S_n: f(i)\not = i\ \mbox{for}\ 1\leq i \leq n\}$, where ...