questions regarding the re-orderings of some finite set of objects.
0
votes
1answer
16 views
permutation with restriction - no two zeroes can be together from an set consisting of 3 zeroes
I have this as data set - 0 1 0 1 0
now how to find out the number of permutations with restriction that no two zeroes can be together.
i.e. 00110, 00011, 11000 ...
2
votes
2answers
43 views
Listing subgroups of a group
I made a program to list all the subgroups of any group and I came up with satisfactory result for $\operatorname{Symmetric Group}[3]$ as
...
0
votes
1answer
18 views
Arrangement of objects in 2 intersecting circles
In how many ways can 8 tennis balls and 8 baseballs be arranged in 2 intersecting circles (much like on the perimeter of a Venn diagram), if there is a ball placed at each of the 2 intersections of ...
1
vote
0answers
29 views
arrangement of objects in circle (circular permutation)
I know circular arrangement of $n$ different objects can be done is $(n-1)!$ ways.
For example :-
I arranged $7$ objects in circle
This can be done in $720$ ways (using $6!$)
$1$) Can I also do ...
-1
votes
0answers
32 views
Selecting a representative permutation
If we have a complete set of permutations {m} = n choose k, how do I select a representative set of permutations in a stream at random such that the selected set say, {s} keeps growing to include ...
2
votes
1answer
127 views
Permutations of a set with a conditional subset
Using the digits 1, 2, 3, 5, 6, 8, 0 only once, how many 4-digit numbers could be constructed if the number is even?
This is an exercise from an online course I'm taking. The given solution suggests ...
0
votes
0answers
37 views
Currency, coin value setter method
The Government of Byteland has decide to issue new currency notes with special protection features to so as to commemorate a great mathematician.
It has decided to issue notes summing up to N and all ...
2
votes
3answers
495 views
Exponential Generating Functions For Derangements
I have been introduced to the concept of exponential generating functions a few days ago. However, my understanding of them are still quite limited, and I would like to see some examples. Earlier this ...
1
vote
3answers
35 views
formula of pascal's triangle
I want to make a program for pascal's triangle,I was reading through the details and found something like this:
...
1
vote
1answer
32 views
Computing the order, inverse, and parity of a permutation
How do you compute the order, inverse and parity of $\alpha=(12)(43)(13542)(15)(13)(23)$? Please explain all steps taken to get the answer.
I guess my thought process was to first put it into a ...
0
votes
0answers
26 views
Calculating the probabilities of different lengths of repetitions of numbers of length 6
This question is similar to the question I asked here: Calculating the probabilities of different lengths of repetitions of numbers of length 4
except now I'm having problem with numbers of length 6.
...
3
votes
2answers
54 views
Unable to get to all permutations after $n-1$ transpositions
Problem: Give an example of a permutation of the first $n$ natural numbers from which it is impossible to get to the standard permutation $1,2,\ldots,n$ after less than $n-1$ transposition operations ...
0
votes
2answers
280 views
Irreducibility of the standard representation of $S_n$.
The permutation representation of $S_n$ is $\mathbb C^n$ with elements of $S_n$ permuting the basis vectors $\{e_1, e_2, \ldots, e_n\}$. It has a trivial subrepresentation spanned by the vector $v = ...
4
votes
1answer
47 views
Action of $S_7$ on the set of $3$-subsets of $\Omega$
Reviewing the great book in Permutation Groups by J.D.Dixon, I encountered the following problem:
Show that $S_7$ acting on the set of $3$-subsets of $\Omega=\{1,2,3,4,5,6,7\}$ has degree $35$ and ...
1
vote
2answers
73 views
Product of permutation matrices
I want to prove that the product of two permutation matrices is itself a permutation matrix. But I don't know how. Please help!
1
vote
1answer
41 views
Permutation combination problem
This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6
of the 9 numbers randomly selected are printed such that no two tickets have the same set of ...
2
votes
1answer
31 views
What is the professional term for the combination of the selection in n out of the total m elements?
I know the number of combinations is called ${}_nC_r$, but what about all the exact outcomes?
For example: I have $3$ elements $a,b,c$ and for the parameter $2$, I will have outcomes
$$ab,\quad ...
6
votes
1answer
40 views
Grouping natural numbers into arithmetic progression
I need to find the number of ways of dividing the first 12 natural numbers into 3 equal groups (4 numbers each), so that the numbers in any particular group can be arranged in AP (Arithmetic ...
0
votes
1answer
24 views
Combination of arrangement and probability
Four guys and four girls are arranged in a row such that no two girls are together. What is the probability that any two of the four guys are together?
1
vote
1answer
24 views
possible combinations of 3-digit
How many possible combinations can a 3-digit safe code have?
Because there are 10 digits and we have to choice 3 digits from this,
then we may get $10^P3$ but A author used the formula $n^r$, why is ...
0
votes
3answers
30 views
permutation/combination problem
There are 3 doors to a lecture room. In how many ways can a lecturer enter the room from one door and leave from another door?
I have done like this: They way of entering is 3 and exiting is also
...
5
votes
1answer
58 views
Is there a name for this given type of matrix?
Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$?
(The motivation for this ...
2
votes
2answers
23 views
Calculating permutations if the sequences have to be in ascending order?
How would you go about calculating the number of permutations in ascending order.
Obviously if you had (a set of) 3 numbers you have $ 3! $ permutations:
(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), ...
1
vote
3answers
57 views
The number of words that can be made by permuting the letters of _MATHEMATICS_ is
The number of words that can be made by permuting the letters of MATHEMATICS is
$1) 5040$
$2) 11!$
$3) 8!$
$4) 4989600$
First of all I do not understand the statement of the problem, I would ...
-2
votes
1answer
58 views
Show that there does not exist a permutation α in S4 satisfying (1 2)(3 4)α = α(1 2 3 4)? [closed]
Let $f=(1 8 )(3 6 4)(5 7)(2)$ and $g=(1 2 3)(4 5)(6 7 8)$ find signature of $f$. if there is a $α$ in $S_8$ such that $αf= gα$. Give reason for your answer.
2
votes
1answer
22 views
Number of Total orders of a dependency graph
Define a dependency graph to be a graph $G=(V,E)$ such that an edge between vertices $v$ and $u$ in $V$ is present if $v<u$ i.e. $v$ comes before $u$ in our ordering (I'm not very concise here, I ...
0
votes
2answers
34 views
Determine no of combinations for cutting stock algorithm
I have to buy $n$ wooden logs of size 2000 each, from which I have to cut different pieces of smaller size say:
255*10
750*7
550*13
In a manner that cutting will ...
5
votes
1answer
114 views
Why is $S_5$ generated by any combination of a transposition and a 5-cycle?
Why is $S_5$ generated by any combination of a transposition and a 5-cycle? Is this true for any prime $p$ (in this case $p=5$)?
1
vote
1answer
21 views
Is it possible to divide n in d parts where each part can have a specific range of values?
Given a value n and number of parts d.
Each part has max and min values it can have.
Is it possible to divide n in d parts fullfilling the max and min value criteria
?
Example
d=2 n=5
Part 1 ...
1
vote
2answers
66 views
Permutations of a queue of interlaced boys and girls.
Suppose $5$ boys and $4$ girls are to be arranged in a queue such that between any
two boys there is at least one girl. Find the number of such arrangements possible.
What i think is $5$ boys ...
2
votes
6answers
52 views
calculate the number of possible number of words
If one word can be at most 63 characters long. It can be combination of :
letters from a to z
numbers from 0 to 9
hyphen - but only if not in the first or the last character of the word
I'm trying ...
2
votes
2answers
35 views
From Combination to Permutation
I am facing a (probably) basic counting issue.
If $P(n,r)$ the permutations for $r$ objects from $n$ and $C(n,r)$ the combinations, we have : $P(n,r) = r!C(n,r)$.
Yet there are two example in which ...
0
votes
0answers
57 views
Ball and holder problem [duplicate]
I am trying to solve this but having a tough time deriving the formula.
There are $X$ ball and $Y$ holders $Y \leq X$. Out of the $X$ balls, $N$ are red and $X-N$ are blue.
What is the probability ...
1
vote
2answers
32 views
Number of length-five words
How many length-five words can be written using two A's, two T's and one E?
Why is it not $\binom5 2 \times\binom 5 2 \times \binom 5 1$?
Is it $ \binom 5 3 = 10$?
2
votes
4answers
269 views
Number of mixed doubles pairs such that no one plays with his/her spouse?
Can you help me with this problem?
There are $7$ married couples. What will be the number of mixed double pairs in tennis such that no one plays with his/her spouse?
Can some one help me with ...
12
votes
3answers
4k views
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?
I have a homework problem in my textbook that has stumped me so far. There is a similar one to it that has not been assigned and has an answer in the back of the textbook. It reads:
How many ways ...
1
vote
1answer
30 views
Need an algorithm to compute number of elements in sample space
An urn contains $X$ red balls, $Y$ green balls, and $Z$ white balls. $N$ balls
are drawn without replacement from the urn, and the colors are noted in sequence.
$N \leq X+Y+Z$
Trying to come up ...
1
vote
0answers
36 views
Proving $Perm(S)\cong Perm(T)$
I am trying to prove this proposition:
Let $f:S\to T$ be a bijection of sets. Then $Perm(S)\cong Perm(T)$.
I clearly want to show that $\phi: Perm(S) \to Perm (T)$ is an isomorphism with, $\sigma ...
0
votes
0answers
31 views
How do I make a function where the range of the function is a permutation of the given function domain?
An example for 0, 1, 2, 3, 4, 5 would be:
f(0)=5;
f(1)=1;
f(2)=0;
f(3)=4;
f(4)=2;
f(5)=3;
I have found f(x) = 911 * x % N to work where 911 can be any large ...
1
vote
1answer
332 views
Permutation identities similar to $(7901234568 / 9876543210) \cdot 1234567890 = 0987654312$
It is well known that $9876543210/1234567890 = 109739369/13717421 = 8.0000000729...$
(See for example)
Recently I posted at
http://list.seqfan.eu/pipermail/seqfan/2012-October/010235.html
my ...
1
vote
1answer
23 views
Dice Roll Permutation Problem
Here is my problem:
You have a standard dice, with possible rolls: $\{1, 2, 3, 4, 5, 6\}$. How many permutations exist in 10 rolls such that no two immediate rolls are the same?
For example:
$\{1, ...
3
votes
4answers
96 views
What is the order of $\tau = (5\ 6\ 7\ 8\ 9)(3\ 4\ 5\ 6)(2\ 3\ 4\ )(1\ 2)$? Is $\tau$ an even or an odd permutation?
In $S_9$, what is the order of $\tau = (5\ 6\ 7\ 8\ 9)(3\ 4\ 5\ 6)(2\ 3\ 4)(1\ 2)$? Is $\tau$ an even or an odd permutation?
For the first question: I tried to write $\tau$ as the composition of ...
8
votes
0answers
58 views
Expression of basis vectors of permutation modules in different bases.
Write $[n]:=\{1,\ldots,n\}$. For a partition $\lambda\vdash n$, I will write $[\lambda]$ for the Specht module that corresponds to $\lambda$, i.e. the complex vector space spanned by all standard ...
1
vote
1answer
58 views
Permutation & Combination - how many numbers smaller than $2.10^8$ and are divisible by $3$ can be written by means of the digits $0$,$1$ and $2$
How many numbers smaller than $2.10^8$ and divisible by $3$ can be written by means of the digits $0$,$1$ and $2$?
Left Zero padding not allowed.
I am getting this as -
3 digits - 2*3 = 6
4 digits - ...
0
votes
1answer
42 views
Counting Methods: Restricted Permutations
I have been scratching my head for a long time. The question is: How many words can be formed using all letters in the word EXAMINATION in such a way that the first two letters are different ...
1
vote
3answers
62 views
The number of bijections $f$ of $\{1, 2,…, n\}$ such that $f(i) \ne i$ for any $i$
Show that the number of bijections $f$ of $\{1, 2,..., n\}$ such that
$f(i) \ne i$ for any $i$ is equal to $$\sum_{j=0}^{n}(-1)^j\frac{n!}{j!}.$$
Can I get some help for the above problem? I am ...
2
votes
1answer
45 views
Permutation & Combination - How many 4 digit no's are there whose decimal notation contains not more than two distinct digits?
How many 4 digit no's are there whose decimal notation contains not more than two distinct digits?
1
vote
2answers
87 views
Can you find an isomorphic group?
Let $G$ be a group with elements $\{e, a, b, c, \theta, \theta a, \theta b, \theta c \}$ where $a^2 = b^2 = c^2 = \theta$, $\theta^2 = e$, $ab = \theta b a = c$, $bc = \theta c b = a$, $ca = \theta a ...
2
votes
2answers
58 views
At least two people have the same birthday
If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday?
I tried solving ...
1
vote
1answer
27 views
On permutations and Combinations
$mn$ squares of equal size are arranged to forma a rectangle of dimension $m$ by $n$, where $m$ and $n$ are natural numbers.
Two squares will be called 'neighbours' if they have exactly one common ...
