Permutation Definition and 276 Threads

Homework Statement Find the PA = LDU factorizations for: A = \left[ \begin{array}{ccc} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 2 & 3 & 4 \end{array} \right] The author chooses a permutation matrix : P = \left[ \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] If I do...

Given a countably infinite set, A, is the set of all permutations of A also countably infinite?

Homework Statement how many ways can 10 people sit around a roundtable if 3 particular people sit together Homework Equations The Attempt at a Solution my attempt was (8-1)! x 3!

There are 8 people in a line to see a movie. A,B,C are in the line. What is the probability that A is in between B and C? (I can explain more, but don't want to throw in too much to confuse). BTW there is 8 people in the line.

Hi there, i was wondering if you had any thoughts on the following question: Let (a_{1}, a_{2}, ..., a_{2n}) be a permutation of {1, 2, ..., 2n} so that |a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}| , whenever i \neq j . Show that a_{1} = a_{2n} + n, if 1 \leq a_{2i} \leq n for i = 1,2, ..., n

the group of permutations on 9 elements (1,2,3,4,5,6,7,8,9) Can any I tell me how can I make a multiplication between permutations, and to take some power to permutations? also, how can I show that determines the order of the permutation. Many Thanks.

Define two subgroups of S6: G=[e, (123), (123)(456)] H=[e, (14), (123)(456)] Determine whether G and H are isomorphic. It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be...

idk if i should post this question here as i couldn't find any specific forum to post at homework section this has to do with statistics. the question is: Question: The Board of a company consists of 4 men and 4 women.The 8 directors are to stand in a straight line so that a photo can be...

I am sure this is very simple but I m kind of confused here. What is this product equal to and what's the order of the permutation? (1 2 3 4 5 6 7) (3 6 7 4 2 5 1) I thought it was (3 7 5 2 6 1 4) but I am reading somewhere that it should be (137)(265)(4) and hence has order 3. Why...

1. 3-digit numbers are constructed from the digits 0,1,2,3,4,5,6,7,8,9 using each digit at most once. How many such number are divisible by 5? 2. Just simply permutation, the answer is 136. 3. 8 x 7 x 2 = 128

hi if P and Q are 2 permutations of X, their product, P.Q, is the permutation of X (X=1,2,3,4,5), obtained by following the mapping Q with the mapping P. if Q=2 3 4 1 5, and P is 1 2 5 3 4, then how do i find P.Q and Q.P ? i have tried a few mappings but can never get the same answer as in...

If A is a cycle, and A=(1 4 5) (2 3 6). Is there a B such that BAB^-1=A^2. I found A^2=(1 5 4) (2 6 3), but I'm not really sure where to go from there.

I have two questions, they aren't homework questions but I figured this would be the best place to post them (they are for studying for my exam). Homework Statement How many elements of S_6 have order 4? Do any elements have order greater than 7? Homework Equations S_6 is the...

Homework Statement prove that there are not permutations of order 18 in S_9. Homework Equations The Attempt at a Solution let t=c_1,...,c_k is cycle decomposition of such permutation. let r_1,...,r_k the orders of c_1,...,c_k. then lcm(r_1,...,r_k) = 18 and r_1+...+r_k = 9...

Homework Statement Prove that there is no such permutation a such that (a-inverse)*(1,2)*(a) = (3,4)(1,5) The Attempt at a Solution Does it have something to do with the order of (1,2)? I know the order is 2, so if we square (a-inverse)*(1,2)*(a), then we get the identity...how else...

Homework Statement Let G be the group S_3. Find the permutation representation of S_3. (Note: this gives an isomorphism of S_3 into S_6) The Attempt at a Solution Is there only ONE permutation representation, because the question asks for "the" p.r. I don't know where to start.

I'm trying to show that for two permutations f ang g in Sn, the number of disjoint cycles in fg is the same as the number of disjoint cycles in gf. I know that in general fg does not equal gf, but by working examples it seems like they always decompose into the same number of disjoint cycles...

1. The problem statement and attempt at solution Hey, I'm still trying to get my head around indicial notation. I'm finding it quite hard.. I think this is somewhat right, but I don't know if the answer is clear enough.. Any hints/comments are greatly appretiated! Thank you

Homework Statement Find the number of arrangements possible for arranging m+n things in a circular orientation, such that m things are alike and th other n things are also alike but of diffrent kind as from the first category. Attempt: I fix one thing. I am left with m+n-1 So the...

Homework Statement There are 5 girls and 2 boys. A committee of 3 members is to be formed such that there is at least one boy in the committee. Find the number of ways of doing so. The Attempt at a Solution One place is fixed for a boy. So choosing one boy out of 2: 2C1 I am left...

Homework Statement Arrange the letters of the word daughter such that 1. no two vowels are together. 2. the relative positions of the consonants and the vowels are not changed. The Attempt at a Solution 1. Total arrangements =8! Ways in which at least 2 vowels occur...

a small permutation question...just don't get the right answer question: 12 differently coloured beads are arranged around a necklace. how many different arrangements are possible? the right answer on back of the book is 19958400 not 11! don't know why may be the book was wrong, can anyone...

Homework Statement Consider the word MATHEMATICS. There are some vowels: AEAI The remaining 7 letters are MTHMTCS. Find the number of different 11 lettered words formed from these particular letters (repetition not allowed) such that all the vowels occur in the same order AEAI. For example...

How do you write the permutation and combination formulas using latex. This is the best I can do: n_P_r=\frac{n!}{(n-r)!}

Homework Statement a. Find the permutation representation of a cyclic group of order n. b. Let G be the group S3. Find the permutation representation of S3. Homework Equations n/a The Attempt at a Solution I unfortunately have not been able to come up with a solution. I really...

Homework Statement Let n \geq1. Let <a1,...,as> \inSn be a cycle and let \sigma\inSn be arbitrary. Show that \sigma\circ <a1,...,as> \circ\sigma^{-1} = <\sigma(a1),...,\sigma(as)> in Sn. Homework Equations The Attempt at a Solution As the title says, i believe this is a...

Homework Statement Let a and b belong to Sn. Prove that (a^-1)(b^-1)(a)(b) is an even permutation. Homework Equations Definitions I have are Every permutation in Sn, n>1 is a product of 2 cycles and A permutation that can be expressed as a product of an even number of 2 cycles is...

Homework Statement Prove that the number of permutations p on the set {1,2,3,...,n} with the property that |p(k)-k| \leq 1, for all 1\leqk\leqn, is the fibonacci number f_{n} The Attempt at a Solution I guess I don't understand what it's asking. I thought I knew what a permutation was...

Homework Statement I'm taking a Magnetic Fields class, and the professor taught us doing cross and dot products using the permutation index. But I don't quite understand how it works completely. I have these problems: Given: \vec A=\hat x + 2\hat y - 3\hat z \vec B=3\hat x - 4\hat y...

Hehe, I'm working through the complete groups books right now, so don't think I ask you all my homework questions... I'm doing a lot myself too =). Homework Statement 1) If H is a subgroup of S_n, and is not contained in A_n, show that precisely half of the elements in H are even permutations...

This is problem 4 from section 2.3 of Fundamentals of Probability by Saeed Ghahramani. Homework Statement Robert has eight guests, two of whom are Jim and John. If the guests will arrive in a random order, what is the probability that John will not arrive right after Jim? Homework...

Homework Statement in how many different ways can 7 different books be arranged in a row if a. 3 specified books must be together, b. two specified boks mus occupy both ends Homework Equations i don't udnerstand wether it is a permutation or a combination. The Attempt at a...

Can you tell me if my answer is correct? in (1 2 3 4) (1 2 3 4) The order of permutation is LCM = (4, 4) = 8

Homework Statement If n>= 3 and S(n) is the symmetric group on n letters. prove every odd permutation in S(n) can be written as a product of 2n+3 transpositions, and every even permutation can be written as a product of 2n + 8 transpositions. Homework Equations The Attempt at a...

I can't really imagine how this was approached. Let P_{\alpha0} fixed P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\epsilon_{\alpha0}\sum_{\alpha}\epsilon_{\beta}P_{\beta}=\epsilon_{\alpha0}A I can understand that P_{\alpha0}P_{\alpha} =...

Homework Statement I can't really imagine how this was approached. Let P_{\alpha0} fixed P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\epsilon_{\alpha0}\sum_{\alpha}\epsilon_{\beta}P_{\beta}=\epsilon_{\alpha0}A Homework Equations...

Homework Statement 6 men and 3 women are arranged in a line Find the number of ways: A)That they can be arranged without any restrictions B)They can line up with no 2 women next to each other Homework Equations The Attempt at a Solution A)Well that is simply 9! B)This is where...

Homework Statement let there be a and b (b taking any value) two permutation with the same grade .demonstrate that ab=ba <=> a=e(e=the identical permutation) . Homework Equations e=(1234) (1234) The Attempt at a Solution Don't have a clue with what to start/end

Homework Statement what is the order of k-cycle (a(1),a(2),...,a(k)) Homework Equations The Attempt at a Solution According to the theorem of the order of a permutation: the order of a permutation set written in disjoint cycle form is the least common multiple of the lengths...

Homework Statement There are 10 different coloured gems will be given to 6 students according to their marks. The marks of the students are 60%,12%,12%,12%,12%,12%. The number of gems obtained is according to their marks. How many ways can it distribute the gems? 2. The attempt at a...

Homework Statement In How many ways can six men and two boys be arranged in a row if: a. The two boys are together? b. The two boys are not together? c. There are at least three men separating the boys? Homework Equations P= N! (n-r)! Identical n objects...

In how many ways the letters in the word PARALLEL can be arranged so that there will always be two "L"s together as in the original word? I have asked this question in yahoo answers. None of them have come out with the right answer. Amazing! It's such an easy problem.:eek:

Permutations of subsets with like objects Question Hello, I'd like to know if I solved the question correctly; if not, I'd appreciate some help. Question: Calculate the number of permutations for a subset of 3 objects from a superset of 8 objects where 5 are alike. My solution attempt...

Maybe I'm just being dense, but I've been having issues with the multiplying non-disjoint permutation cycles (as you may have guessed from the topic title). Simple products like (1, 4, 5, 6)(2, 1, 5) [an example from my textbook], as well as in the opposite order. Mayhap that I'm tired...

How do I calculate all possible permutations of an array of length n? If I draw on a paper, I can do myself permutations of 3 or 4 length arrays. However, I want an algorithm to calculate all possible permutation. And calculate it as fast as possible. Do you know how to do it? I would...

Can someone help me understand this one? The problem is: Four beads-red,blue,yellow, and green-are arranged on a string to make a simple necklace as shown in the figure. How many arrangements are possible? The answer in the book is 3, but I don't get it. I thought it woud be a permutation...

i recently had my A levels exam and was stuck at a question there are 8 balls in a box, 3 are similar and the rest are different, how many ways can 3 balls be chosen if the order of picking out the balls is not important its worth 4 marks, and i do not know where to start even.:frown:

hi all I have a simple question relating to permutation matrices. We have an a matrix, X. We have a permutation matrix, P. We can get the permuted version of X by doing permutedX = P*X*P'. Now, I want to represent the matrices in vector form. The way the books mention it as follows. They...

How many permutation of abcde are there in which ... confused! Hello everyone I'm lost on this problem, it says: How many permutations of abcde are there in which the first character is a, b, or c and the last character is c, d, or e? They say: The number of elements in a certain set can...

Here is the problem concerning permutation groups: u = 1 2 3 4 ------- 3 4 2 1 Show that there is no p such that p^2 (the second permutation) = uI've tried just substituting values for p1, p2, p3 and p4 in: 1 2 3 4...