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

learn more… | top users | synonyms

0
votes
2answers
33 views

Difference between permutations

Given the following: 1) Is it wrong to say (1 2 4) (5 3) = (1 2 4) (5 3) or = (3 5) (1 2 3) ? 2) What is meant by ( 1 2 3 4 5 ) and 1 2 3 4 5 ? And why are they not equal? Thanks!
0
votes
1answer
21 views

Permutation Multiplication (easy)

Given α◦β=(1532)(14)(35) How do we get from the given to = ( 1 4 5 2 ) ( 3 ) = ( 1 4 5 2 ) = (4 1 3 5 2) ? Thanks
0
votes
1answer
65 views

List all the permutations of {1,2,3,4}. Which are even, and which are odd?

The answer is: There are 24 permutations. The 12 even permutations are: id , (1 2 3 4) , (1 3 2 4) , (1 4 2 3) , (1 2 3) , (1 2 4) , (1 3 2) , (1 3 4) , (1 4 2) , (1 4 3) , (2 3 4) , (2 4 3). The ...
2
votes
2answers
71 views

Powers of permutation matrices.

Let $P$ be a permutation matrix obtained by the identity matrix by switching 2 rows $n$ times, (with no two rows switched more than one time). How to show that $$P^{\ n+1} = I$$? Is it true that, ...
1
vote
1answer
38 views

number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle

You are given $1\times2$ rectangles and you have to construct an $n\times2$ rectangle from it. Tell the number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle
2
votes
2answers
43 views

A man, woman, boy, girl, cat, and dog are walking down a path..

I'm hoping someone can explain how this works. The problem: A man, woman, boy, girl, cat, and dog are walking down a path in single file. How many ways can this happen if the dog is between the man ...
1
vote
0answers
15 views

Composing permutations in factorial notation

Given two permutations $p_1$ and $p_2$ in factorial notation, is there a direct algorithm which computes their composition directly, i.e. without translating to a different notation or via computing ...
12
votes
0answers
113 views

Involutions, RSK and Young Tableaux

Let $S_n$ be the symmetric group on $n$ elements. The Robinson-Schensted-Knuth (RSK) correspondence sends a permutation $\pi\in S_n$ to a pair of Standard Young Tableaux $(P,Q)$ with equal shapes ...
0
votes
0answers
24 views

Number of permutations with double restriction

Task is as follows: Let's have 6 element set, there are obviously $6!$ permutations of this set, but there are two restrictions: element 1 and 2 have to be in one cycle and element 3 can't be with 1 ...
0
votes
2answers
26 views

How many good words are there?

A “good” word is any seven letter word consisting of letters from $\{A,B,C\}$ (some letters may be absent and some letter can be present more than once), with the restriction that $A$ cannot be ...
1
vote
1answer
44 views

Why is this the method to getting transpositions from disjoint cycles?

I have the disjoint cycle: $$(156)(2437).$$ Apparently the "method" would get us: $$(1,6)(1,5)(2,7)(2,3)(2,4).$$ Basically you take the first number, and put it as a transposition of the last number ...
0
votes
0answers
21 views

A coin is tossed m+n times.(m>n) How many outcomes have at least m consecutive heads?

The problem I face is(obviously for which the question was intended) that, suppose $m=3$,$n=2$, then ${HHH,H,T}$ and ${H,HHH,T}$ are same while ${HHH,T,H}$ and ${H,T,HHH}$ are different. Hence, I ...
2
votes
1answer
38 views

How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?

As the title states, the question is: "How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?" I don't really get what the problem ...
0
votes
0answers
31 views

Calculating probabilities for distributing M balls in 4 bins scenario

I have the following scenario that I need to obtain the formula for it in order to program it: There are number of balls (M balls), and there are 4 different bins (Bin1, Bin2, Bin3, Bin4) that the ...
1
vote
3answers
24 views

Combination with repeats

I've been stuck for a while on this question and haven't found applicable resources. I have 10 choices and can select 3 at a time. I am allowed to repeat choices (combination), but the challenge is ...
0
votes
1answer
21 views

Permutation and combination regarding two people together

You have 11 friends and can invite 5 to dinner 1) in how many ways if two of the friends married and will not attend separately? 2) in how many ways if two of them are not on speaking terms and will ...
1
vote
2answers
22 views

Permutation of numbers and function

Let $N(x)$ denote the number of terminating zeroes of the number x. If A,B,C is a permutation of the numbers $211^{19}+9$, $9^{101}-9$, and $19^{111}-9$ such that $N(A)<N(B)<N(C)$, determine the ...
0
votes
1answer
14 views

Prove that cyclic index of this operation can be expressed by formula

Let $T_1$ and $T_2$ be disjoint finite sets and let $G_1$ and $G_2$ be, respectively, some groups of permutations of this sets. Direct sum $G_1 \bigotimes G_2$ acts on $T_1 \cup T_2$: $$ \langle ...
0
votes
1answer
10 views

Permutation/Combination question. help needed

How many ways are there to split 4 red, 5 blue and 7 black balls among 1) two boxes without any restrictions
1
vote
1answer
37 views

How to assign values to letters to create unique values per word when all letters are added together?

I'm writing a program to match anagrams in order to practice coding. One way I want to try this is to assign values to letters such that adding up the letters in the individual words creates a unique ...
0
votes
2answers
51 views

Permutations of 7 numbers less than 50

How many solutions does the equation $a + b + c + d + e + f + g ≤ 50$ have if each variable must be a non-negative integer? I feel that the answer is $50 \choose 7$? but that seems far too simple.. ...
0
votes
1answer
20 views

Clarification on the variables used in combination formula

Consider an ant that is walking on a Cartesian grid, starting at (0,0) and ending at (10, 15). The ant always chooses to walk exactly one unit either up or to the right (towards his destination) ...
3
votes
1answer
45 views

What is the value of $1 + {{}^nP_2}/2 +{{}^nP_3}/3 + ~… ~ {}^nP_n/n $

What is the value of $1 + {{}^nP_2}/2 +{{}^nP_3}/3 + ~........... ~ {}^nP_n/n $ ${}^nP_r = \frac {n!} {(n-r)!}$ Attempt: $1 + {{}^nP_2}/2 +{{}^nP_3}/3 + ~........... ~ {}^nP_n/n $ $= 1 + \frac ...
0
votes
3answers
54 views

Permutations and Combinations

A fair $6$-sided die is rolled 5 times and the result is recorded for each roll. How many different results are possible? Of the possible results, in how many ways can there be a result containing ...
2
votes
1answer
42 views

Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.

I am trying to find the smallest positive integer $n$ such that $S_n$ contains an element of order 60. I know that every permutation in $S_n$ can be expressed as the product of disjoint cycles, and I ...
1
vote
1answer
32 views

Left Regular Representations of a Group

The definition in my book gives it as $\lambda_x$ such that $\lambda_xg=xg$.I understand this much. But my question asks to find the left regular representation of $\mathbb{Z}_3$ in $S_3$. I don't ...
0
votes
1answer
21 views

Permutations of a sequence of words

I've been given a question in class and I just wanted to confirm the answer ...
1
vote
1answer
36 views

Find the number of elements in the set: $A=\{\sigma\in S_4 |\thinspace \sigma\thinspace(3)=3\}$

Find the number of elements in the set: $A=\{\sigma\in S_4 |\thinspace \sigma\thinspace(3)=3\}$ I know that this would be $3!=6$. But are these the correct elements? $$ \{e, (12), (24), (14), (142), ...
1
vote
1answer
26 views

Combinations formula

What is the no. of ways to distribute N identical objects among two persons such that at every instant first person gets more than the second person? My approach is : For N=1 ans=1 For N=2 ans=1 For ...
1
vote
0answers
28 views

Using permutations to determine whether given arrangements of the “eight puzzle” are possible.

The "eight puzzle" is a reduced 3x3 version of the 4x4 "fifteen puzzle", which is a very simple game which involves sliding 15 numbered tiles around 16 places, with one free space always being ...
0
votes
1answer
32 views

Showing that there is a permutation $\rho$ that fixes a number that $\sigma$ moves when $\rho \sigma \rho^{-1}=\sigma^{-1}$

Doing an assignment, getting a bit frustrated with this exercise, would really appreciate some help. The first exercise explains what $\sigma$ and $\rho$ are: Let $\sigma$ be the $r$-cycle ...
2
votes
2answers
74 views

Is there a solution to this Seating Plan problem?

So a colleague asked me for some Help on an interesting Problem, which we both couldn't find the optimal answer for. The event which needed it is already in the past, so this is just me trying to ...
0
votes
0answers
22 views

Count of binary matrices having number of ones in each row less than or equal to A and number of ones in each column less than or equal to B?

Example: for $N = 2, M = 2, A = 0, B = 0$, we have only one possible matrix. $$ = \left[ \begin{array}{cc} 0 & 0 \\ 0 & 0 \\ \end{array} \right] $$
1
vote
1answer
68 views

How many ways to paint a board with 2 colors..

You got a fence, you need to paint the boards with black and white, but can not have 3 or more boards same color in a row. how many ways do you have?
1
vote
1answer
44 views

Using that $G$ is isometric to a subgroup of $S_G$ to prove something about $G$

I am doing the following exercise for an assignment: Assume that $G$ is any finite group with non-trivial elements such that $bab^{-1}=a^{-1}$. Let $k$ be a natural number and use induction to ...
0
votes
2answers
26 views

Permutation and combinatorics problem

How many numbers between 10 and 1000 can be formed using digits 3,4,5,7? Should we first find number of 2 digit numbers and then find number of three digit numbers and add them
0
votes
2answers
22 views

every k cyclic is a product of at least k-1 distinct tranpositions

There is a theorem says if $A$ in $S_n$ is a $k$ cycle, and $A = a_1 a_2 a_3 \dots a_m$, where $a_i$ are transpositions, then $m \geq k-1$. But how to show there are at least $k-1$ distinct ...
2
votes
3answers
107 views

In how many ways can the couples sit?

$4$ married couples are to be seated on a circular table with $8$ identical seats. In how many ways can they be seated so that (i) males and females sit alternately and (ii) no husband sits adjacent ...
3
votes
3answers
82 views

How many different 4 digit combinations will include at least one 7, assuming numbers cannot repeat

I cannot get the correct answer - $2016$. What I have tried so far is thus: the number $7$ can occur $1, 2, 3,$ or $4$ times. Since it is a combination we do not care if the number starts with zero ...
3
votes
3answers
168 views

What does “order matters” regarding permutations refer to?

I psychoanalyze EVERYTHING and permutations/combinations are frustrating me. Sorry for posting so many questions lately but I really appreciate all of the help! Ok so I know the permutation formula: ...
0
votes
1answer
27 views

Can someone please explain the reasoning for this permutation problem?

I'm studying and reading through my discrete math book.. I seemed to be grasping the idea of permutations, but I don't understand how the solution for this particular problem came to be. Question: ...
1
vote
0answers
27 views

Arrangements of numbers when each can have multiple values?

I feel as though this is fairly straightforward, but I can't figure it out. If I have $n$ numbers, clearly these can be arranged in $n!$ ways. But if each of the $n$ numbers can have a value $v, ...
0
votes
2answers
64 views

Permutations of a letter sequence

I have been given a question about (i think) permutations, it asks to find how many x letter sequences can be made out of a word. I am getting confused because it first asks how many different ...
0
votes
3answers
40 views

Generate a power set by only adding or removing a single element at a time

Is there an algorithm that is capable of generating a complete power set by only removing or adding one element in each step? I'd like it to avoid duplicates, but ordering isn't important. I've tried ...
0
votes
2answers
46 views

How many skew symmetric matrices are possible?

I just heard the term skew symmetric matrix and upon discovering what it was, I thought to myself, "Jeez, there could only be so many of those." I'm not good with the whole permutation thing and this ...
1
vote
1answer
37 views

What mathematical algebra explains sequence of circular shifts on rows and columns of a matrix?

Consider a simple matrix (3X3) with entries thus: [1 2 3; 4 5 6; 7 8 9;] Circular shifts can be performed on any row or any column thus: row-(1/2/3)-(right/left) and column-(1/2/3)-(up/dn) ...
2
votes
2answers
59 views

Find the center of the symmetry group Sn.

Find the center of the symmetry group $S_n$. Attempt: By definition, the center is $Z(S_n) = \{ a \in S_n : ag = ga \forall\ g \in S_n\}$. Then we know the identity $e$ is in $S_n$ since there is ...
0
votes
1answer
62 views

How to show that a permutation form a group?

Given the following $12$ permutations: $\{(1), (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(32)\}$ (a) Show that the 12 permutations form a group. (b) Find ...
3
votes
0answers
45 views

Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
0
votes
1answer
20 views

Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...