Permutation Definition and 268 Threads

Let me phrase the problem in a general way. Given n objects in a set. All the objects can be categorized into k groups such that no two objects from different groups are identical. Objects in the same group are indistinguishable from each other within the group. Number of objects in each...

Homework Statement Consider a team of 11 soccer players, all of whom are equally good players and can play any position. (a) Suppose that the team has just finished regulation time for a play-off game and the score is tied with the other team. The coach has to select five players for...

I am stuck on this. I have three variables (daily, weekly, monthly), they can have a value of yes or no. I need to know the number of possible 'yes' permutations. I use the formula: n! / (n-r)! which yields '6' i.e., 3*2*1 / (3-3)! --> 6/1 = 6 Yet when I do it by hand: count Monthly...

Homework Statement Prove using the Levi-Civita Tensor/Kroenecker Delta that: (AxB)x(CxD) = (A.BxD).C-(A.BxC).D Homework Equations εіјkεimn = δjmδkn – δjnδkm (where δij = +1 when i = j and 0 when i ≠ j) The Attempt at a Solution if E = (AxB) then Ei = εіјkAjBk, and if F =...

Circular Permutation?? if there are 7 boys and 5 girls, how many circular arrangements are possible if the ladies do not sit adjacent to each other.??

Homework Statement Determine all possible ways to placing three balls into three boxes, where there may be more than one ball in anyone of the three boxes. Could you determine all possible ways of placing 20 balls in 365 boxes? Homework Equations The Attempt at a Solution I know this problem...

Homework Statement Prove that 1/2 P(2,1) + 2/3 P(3,2)+3/4 P(4,3)+ ... + n/(n+1) P(n+1,n) = (n+1)! - 1 Please help! Homework Equations P(n,r) = n!/(n-r)!The Attempt at a Solution The inequation can be simplified to: 1*1! + 2*2! + 3*3!+ ... + n*n! = (n+1)! - 1 (*) Use the induction method...

Homework Statement ~ Homework Equations product of permutation The Attempt at a Solution i have difficulty understanding this q. why in \sigma there are b1b2...bn new element? why can i insert \tau in the permutation "matrix"?\tauitself is a "matrix"??

A system that runs successfully needs 5 components to function properly. Each component is either operable (o) or inoperable (i). Thus the sequence OOOOi denots a state in which all components except the last component are operable. How many states are possible? I know the answer is 2^5 =...

Homework Statement An analyst is presented with lists of four stocks and six bonds. He is asked to predict, in order, the two stocks that will yield the highest return over the next year and the two bonds that will have the highest return over the next year. Suppose that these predictions...

Find how many 3 digits odd number that can be obtained from the digit 1,2,3,4,5,6,7 if, 1/ Repetition of digits not allowed 2/ Repetition of digits allowed my work 1/ --- the last i digit i have control 1,3,5,7 so 2 remaining digits = 6 P 2 x 4 (4ways)...

Homework Statement This is a worked problem: [PLAIN]http://img409.imageshack.us/img409/4821/14091194.gif The Attempt at a Solution In the answer, how did they get from (1 3 4 9)^7(2 6 8)^7 to (1 3 4 9)^{-1}(2 6 8)? I know that \tau^7 means the permutation \tau repeated 7...

hi guys.. can you help me prove this theorem? Every permutation S_n where n>1 is a product of 2 cycles.. i got a little confused with some books' proof..thnx

Homework Statement I have problems understanding part (f) of the following worked example: [PLAIN]http://img7.imageshack.us/img7/5557/61793282.gif The Attempt at a Solution So in part (f), when calculating (\sigma \tau)^{9000}, how does (\sigma \tau)^{818 \times 11} (\sigma \tau)^2...

Homework Statement "How many 5x5 permutation matrices are there? Are they linearly independent? Do they span the space of all 5x5 matrices?"Homework EquationsThe Attempt at a Solution The first two questions are fairly easy. 5! = 120 P matrices. Since dim(space of all 5x5 matrices) = 25...

Homework Statement This is a problem from a chapter entitled "Permutation Groups" of an abstract algebra text. 1. Let α = ( 1 3 5 7 ) and β = (2 4 8) o (1 3 6) ∈ S8 Find α o β o α-1. 2. Let α = ( 1 3) o (5 8) and β = (2 3 6 7) ∈ S8 Find α o β o α-1. Homework Equations Sn is the set...

Please i need help i am not that good in probability and permutation. The digits of the number 1,2,2,3,6,7,8 can be read to give many 7-digits numbers. Find how many different 7-digit numbers can be made if 1/ There is no restriction on the order of the digits. 2/ The digits 1,3,7(in any...

Homework Statement In how many ways can this selection: {0,1,2,3,4,5} be written in a 3 digit form?(without repetition) Homework Equations The Attempt at a Solution my answer was 120 but the book says it's 100, I am confused.. need help.

Homework Statement \mbox{Prove that}\,g^{ij} \epsilon_{ipt}\epsilon_{jrs}\,=\, g_{pr}g_{ts}\,-\,g_{ps}g_{tr} Notation : e_{ijk}\,=\,e^{ijk}\,=\,\left\{\begin{array}{cc}1,&\mbox{ if ijk is even permutation of integers 123...n }\\-1, & \mbox{if ijk is odd permutation of...

i'm having trouble to show that if P: G1 --> G2 is a group homomorphism, then the image, P(G1) = {g belongs to G2 , s.t. there exists h belonging G1 , P(h) = g}, is a subgroup of G2 Also: Let G be a group, and Perm(G) be the permutation group of G. Show that the map Q : G --> Perm(G) g...

Help with permutation groups... How do i show that if P: G1 --> G2 is a group homomorphism, then the image, P(G1) = {g belongs to G2 , s.t. there exists h belonging to G1 , P(h) = g}, is a subgroup of G2 Also if we let G be a group, and Perm(G) be the permutation group of G. How do i show...

Homework Statement There is a total of 19 students sitting in a semi-cirlce. How many seating arrangements are possible, if 4 of the 19 students have to sit next to each other? The Attempt at a Solution I'm not sure if the calculation is: 15! x 4! or 19! / 4! Thanks!

I'm a bit confused about something. Does the parity of a permutation (i.e. if it is even or odd) tell you if the order of the permutation is even or odd, or are they unrelated? Any insight would be appreciated. Cheers, W. =)

Homework Statement A photographer is positioning 5 men and 4 women for a photo shoot. The men are positioned in the order from shortest on the left to tallest on the right. Find the number of ways the photographer can position them in a row. (All men are of different heights and are not...

Homework Statement 5.4: If sigma in S_n has cycle type n_1,...,n_r, what is sgn(sig)? (sgn is the sign homomorphism)Homework Equations sgn(sigma) = 1 if sigma is even. sgn(sigma) = -1 is sigma is odd cycle type is the length of the cycle type. If n_2 = 2, sigma has two 2-cycles.The Attempt at a...

I am somewhat distracted so this post will not be what it should, given that GAP is one of my interests. For those who don't already know: GAP is a powerful open source software package for computational algebra, especially computational group theory and allied subjects. This long running...

Homework Statement the problem states solve for n. nP4 = 8(nP4) Homework Equations no relevant equat. i can think of? The Attempt at a Solution my attempt at this was nP4 = 8(nP3) idk what i tried to do, but i tried to get it in standard form i guess: n!/ (n-4) = 8(n!)/(n-3) it...

Homework Statement [I] need to compute this permutation in S10 (4 2 1)(5 4 9 10)(2 3 4)(7 1)(3 6) Homework Equations The Attempt at a Solution I can compute it when i put it into 2 rows eg 1 2 3 4 5 6 7 8 9 10 4 1 3 2 5 6 7 8 9 10 that's equal to ( 4 2 1) but doing this out with the above...

For this question, i already solve the part a and part b. For the part c, i try to solve it but i can't get the answer that given. Can someone explain to me? How to do the part c. Thanks!

Homework Statement Let P be a permutation of a set. Show that P(i1i2...ir)P-1 = (P(i1)P(i2)...P(ir))Homework Equations N/A The Attempt at a Solution Since P is a permutation, it can be written as the product of cycles. So I figured that showing that the above equation holds for cycles will...

Homework Statement Let P be a permutation of a set. Show that P(i1i2...ir)B-1 = (P(i1)P(i2)...P(ir)) Homework Equations N/A The Attempt at a Solution Since P is a permutation, it can be written as the product of cycles. So I figured that showing that the above equation holds...

Homework Statement Suppose G is a group generated by the two permutations (1 2 3 4 5) and (1 2)(3 4). Decide which group G is and prove your answer.Homework Equations The Attempt at a Solution So i crunched this out and I found identity 15->2 cycles 20->3 cycles and 24->5 cycles So i think...

Hello! I was wondering if there is a way to generate a permutation matrix P such that each application of P to another matrix A will find the "next" permutation of A. I'm looking for a way to generate a permutation matrix P (size m x m) such that applying it m! times to A (m x m) returns A...

Homework Statement (1 2) (1 4 5) (2 3 4) (2 5)= (1 4) (3 5) Homework Equations The Attempt at a Solution Can someone explain to me how to do this permutation? I know it's the easiest thing to do but i just went blank! how did my professor get (1 4) (3 5)?

A factory has built a robot which moves on all squares of a 6*6 table. There is an arrow On all of the squares of the table when it moves on an square it reads the arrow the square and moves according to the square but before doing that it changes the arrow of the square aim to the previous...

For this problem, I have to find all orbits of given permutation. \sigma: \mathbb{Z} \rightarrow \mathbb{Z} Where, \sigma(n)=n-3 Now, the problem is I do not know how to approach this permutation in the given format. All the permutations I dealt with were in the form: \mu...

Homework Statement Multiply the permutation (246)(12)(47) The Attempt at a Solution This has got to be so easy yet I cannot figure it out on my own. I understand that for (246) it means that 2 \mapsto 4, 4 \mapsto 6, 6 \mapsto 2 . Could anyone lead me on what I should do next with...

Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s geq l − 1. I'm trying to get a better understanding of how to begin proofs. I'm always a little lost when trying to solve them. I know that I want to somehow show that s is...

Homework Statement a computer terminal displaying text can generate 16 different colours numbered 1 to 16. anyone of colours 1 to 8 may be used as the "background colour" on the screen, and anyone of colours 1 to 16 may be used as the " text colours"; however, selecting the same colour for...

Hello, can anyone tell me how to find order 15 in S8. I only know. Permutation (abc)(defgh) have order 15. Next, I would think about 8*7*6*5*4*3*2*1 = 13440 Number of permutations, for order 15 in s8. would be 8*7*6*5*4*3*2*1 / 3*5 = 896. There are 896 permutation of order 15 in...

Hello, can anyone tell me how to find order 15 in S8. I only know. Permutation (abc)(defgh) have order 15. Next, I would think about 8*7*6*5*4*3*2*1 = 13440 Number of permutations, for order 15 in s8. would be 8*7*6*5*4*3*2*1 / 3*5 = 896. There are 896 permutation of order 15...

Hi guys, i have no idea how the Permutation should be used. An example, Find the number of arrangement of all nine letters of the word SELECTION in which a)the two letters E are next to each other Well i can solve this, i just make the EE as one unit so 8P8 b)the two letters E are not...

Homework Statement If you take powers of a permutation matrix, why is some P^k eventually equal to I ? Homework Equations - The Attempt at a Solution From the solutions manual of the book: There are n! permutation matrices of order n. Eventually, two powers of P must...

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...