Permutation Definition and 268 Threads

Hi there I am working through the problems in R.I.G. Hughes book the structure and interpretation of quantum mechanics and have hit a wall in the last part of the following question: Show that Sx and Sy do not commute, and evaluate SxSy-SySx. Express this difference in terms of Sz, and...

Let $N=\{ 1,2,\ldots ,n \}$. As usual, take $S_n$ as the set of all bijections from $N$ to $N$. Corresponding to each element $i$ in $N$ we have a set $E_i \subseteq N$ of "enemies" of $i$. Denote $|E_i|=r_i$. Its also given that: 1) $r_i \geq 0, \, \forall i \in N$ 2) $r_1 + \ldots + r_n \leq...

Homework Statement A crew of an 8 oar boat has to be selected from 11 people, out of which 5 can oar only on one side, 4 can oar only on the other side and 2 can oar on either sides, find in how many ways can the selection be done? The Attempt at a Solution What I did here is assumed...

Homework Statement how many 4 digit numbers are there which do not contain more than 2 different numbers? Homework Equations The Attempt at a Solution all can contain the same digit any 3 out of the 4 places can be occupied by the same digit and any 2 out of the 4 places can...

Homework Statement There are 15 players, out of which 4 players own one 4 seater car each, and the car will be driven by the owner himself. In how many ways can they be seated in the cars? Homework Equations (3n)!/(n!)3 The Attempt at a Solution i know that i have to substitute...

Homework Statement Prove the following: \varepsilon_{ijk}= \left| \begin{array}{ccc} \delta_{1i} & \delta_{1j} & \delta_{1k} \\ \delta_{2i} & \delta_{2j} & \delta_{2k} \\ \delta_{3i} & \delta_{3j} & \delta_{3k} \end{array} \right| Homework Equations From my textbook: \hat{e}_3 = \hat{e}_1...

good day! i need to prove that the alternating group An is a normal subgroup of symmetric group, Sn, and i just want to know if my proving is correct. we know that normal subgroup is subgroup where the right and left cosets coincides. but i got this equivalent definition of normal group from...

Hi. Consider two isomorphic state spaces \mathcal{E}(1) and \mathcal{E}(2). The first belongs to a proton, the second to an electron and they both have the same spin. #Let B(1) be an observable defined on the first space, spanned by |1,u_{i}\rangle, eigenvectors of B(1) with eigenvalues b_i...

Homework Statement How many way can a team lose 3 of their next 5 games? How many ways can a team lose 2 of their next 5 games? Why are the two answers the same? Homework Equations Permutation = nPr = n! / (n-r)! Combination = nCr = nPr / r! where, n, r are non...

hey, i have a quick question about G-sets and how the action of an element of the group on the set can be represented as a permutation of the elements of the set. If you had a set S = {1,2,..,50} and a permutation σ: S→S where |σ|=30, Does this mean that the minimum number of fixed...

All the proofs I have seen for this theorem uses the same argument: First prove that the identity permutation has even parity. Then let a be (one of) the first elements to appear in a transposition representation of a permutation in Sn. Then identify all the other transpositions in the...

Homework Statement I have 6 cards with the digits 1,2,2,3,4 and 5 written on each of them. In how many ways can I arrange 3 out of the 6 cards in a row? Homework Equations The Attempt at a Solution Case 1: Only one card with digit '2' two is taken, so 5P3 =60 Case 2: Both cards with digit...

Homework Statement http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w03_qp_6.pdf question 6 b ii Homework Equations The Attempt at a Solution The concept is bothering me. the answer is 5! × 3! × 4C1. Why is it a permutation problem? Plus why do...

Homework Statement Let Pn denotes the no. of ways of selecting 3 people out of 'n' sitting in a row if no two of them are consecutive and Qn is the corresponding figure when they are in circle . If Pn - Qn = 6 , then 'n' is equal to: The Attempt at a Solution Pn = (n-2) C 3 Qn =...

Homework Statement Find the no. of +ve integral solution of XYZ = 21600

I already have the answer for this, but wondering if there's some efficient way to calculate this. There are 7 identical items, each with a equally random chance of being placed in 1 of 32 containers. What are the possible permutations? 00000000032 = 7 identical items into 1 of 32 distinct...

Find the number of ways of selecting 3 men and 3 women from 5 married couples such that there are exactly 2 married couples. I need the reasoning

Homework Statement I know what's happening with the problem, but I just hate myself drawing all possible arrangements, I think I am too stupid, I hope better solution. Problems: 6 different Cookery books and 8 different History books are put on bookshelf. How many possible arrangements...

1. I think my professor gave me credit for this problem when he shouldn't have! I just want to understand for the test, so I want someone to verify for me. 2. How do you find out whether a given permutation is even or odd without factoring it into transpositions? 3. My answer was: Factor it...

Homework Statement 4 books by Shakespeare, 2 books are Dickens and 3 by Conrad are chosen for the problem. The question is to find the number of ways in which the books can be arranged s.t. the 3 Conrad books are separated. Homework Equations The Attempt at a Solution n(C separated)...

Hey, I just have a small question regarding the conjugation of permutation groups. Two permutations are conjugates iff they have the same cycle structure. However the conjugation permutation, which i'll call s can be any cycle structure. (s-1 a s = b) where a, b and conjugate...

Homework Statement Hello, it is a permutation / combination approach question, however, having thought about an hour i can't get any idea how it should be solved. Question is A coin is flipped n times, where n>=3 Find the number of ways to obtain (i) exactly two heads (ii) at...

Hi to everyone... I would like to know which is the permutation 4661 of the elements G = {1,2,3,4,5,6,7} I have search for the formula around the internet but I could not find it... So I hope anyone can help about this solution. Thank you... and the result on the picture is like this as...

Homework Statement I forget the exact expression of the questions. But the related details are exhaustive here. it's about permutation and combination. By the way, I am not student, i am looking for explanation and understanding, not answers.. 1. There are 6 people, namely A, B, C, D, E...

Use nested for loops to produce the following pattern of cyclic permutations of the English alphabet: abcde...yz bcdef...za cdef...zab ... zabcde...xy HINT: you may find the modulo (remainder) operator % useful. I have an idea of how to do this but it would not use the modulo operator...

(Apologies for the lack of LaTeX formatting - I usually do my typesetting with MathType, but I only have Microsoft Equation Editor on this computer which doesn't have LaTeX export). This isn't a homework question, but is problem I've discovered I'm facing after diving into another problem, but...

Four married couples attend a wedding dinner. One of the couples brought along two children. Find the number of ways in which these ten people can be seated round a table if each couple must sit together. I need to know the logic and thinking process behind how the answer is derived. What I...

Homework Statement How do I determine the parity of a permutation? I think my reasoning may be faulty. By a theorem, an n-cycle is the product of (n-1) transpositions. For example, a 5 cycle can be written as 4 transpositions. Now say I have a permutation written in cycle notation: (1...

there are n students in a class. They are selected in sets of m. A student says he is selected a times. find value of a in terms of m and n. Total number of selections made are nCm. After that nothing is striking in my mind.can you please help.

Homework Statement A test consists of 5 pure math questions A, B, C, D, E and 6 statistics question F, G, H, I, J, K. The examiners want to arrange all eleven questions in a random order such that a pure math question must be separated from another with exactly one statistics question...

Homework Statement Suppose G is a group, H < G (H is a subgroup of G), and a is in G. Prove that a is in H iff <a> is a subset of H. Homework Equations <a> is the set generated by a (a,aa,aa^-1,etc) The Attempt at a Solution For some reason this seems too easy: 1. Suppose a...

Homework Statement The integers 1 through 6 appear on the six faces of a cube, one on each face. If three such cubes are rolled, what is the probability that the sum of the numbers on the top faces is 17 or 18? Homework Equations Probability = # of desired outcomes / total # of outcomes The...

I feel like I'm doing this correctly but my professor gave us an answer that is different from what I'm getting. Composition of (12345)(12345) Reading right to left I get (13524) but the answer he gives is (135)(24) The odd thing is I'm getting the rest of these correct so I don't feel...

Good evening to all I wonder if anyone can help please I have 8 switches b1,b2,b3,b4,b5,b6,b7,b8 I am trying to work out how many permutations I would have if I pressed any 4 of the 8 switches ie if I pressed b1,b3,b,7,b8 to make a circuit or it could be b3,b5,b6,b7 doing it by long hand I...

Hi, I have this problem in which a word (lets say "ABERRATIONAL") is given. Now how many permutations (no unique words) can be made given that the 3 A's have to be next to each other? My solution: regard the 3 A's as one block, so we have 12-3+1 = 10 letters. This gives 10! permutations...

All the perutations of elements in R(3)(three dimension euclidean space) form a permutation group. This group must be E(3)(euclidean group)?

Hi here's a problem I am having. Consider the hilbert space of two-variable complex functions \psi (x,y). A permutation operator is defined by its action on \psi (x,y) as follows. \hat{\pi} \psi (x,y) = \psi (y,x) a) Verify that operator is linear and hermitian. b) Show that...

I'm studying the S_n groups and I've been calculating a bunch of compositions of m-cycles. I haven't, however, been able to find a general pattern in how to do this for arbitrarily complicated cycles. Are there any general composition rules or is there no other way to find the compositions...

Homework Statement Show that if G is any group of permutations, then the set of all even permutations in G forms a subgroup of G. I am not sure where to start - I know there is a proposition that states this to be true, but I know that is not enough to prove this statement.

Homework Statement What is the permutation matrix associated to the permutation of n indices defined by p(i) = n - i + 1? What is the cycle decomposition of p? What is it's sign? Homework Equations Prop. A permutation matrix P has a single 1 in each row and in each column, the rest of its...

Hey all, I recently encountered a problem that I cannot seem to solve... Let's say I have the following coins A, B, C, D and E, each one with an associated integer value such that: A = 1 B = 2 C = 3 D = 4 E = 5 Let's say I can pick N of them, and order does matter (so ABC is not...

Let n ∈ N. Explain what is meant by saying that π is a permutation of n = {1, 2, . . . , n}. The permutation A is given below in two line notation. Write A in disjoint cycle notation.  1 2 3 4 5 3 5 1 2 4  Find A^-1, writing your answer in disjoint cycle notation. Give two examples of...

Homework Statement Let r be a positive integer. For any number x, let (x)r = x(x-1)(x-2)...(x-r+1) Show that (-1/2)r = (-1)rr!2-2r(2r take r) Homework Equations by "2r take r" I mean what is usually denoted by (n / r) (written like a fraction but without the bar) and is calculated...

Homework Statement In a test there were n questions. In the test 2n – i students gave wrong answers to at least i questions where i = 1, 2, 3, …, n. If the total number of wrong answers given is 2047, then n is The Attempt at a Solution I don't understand how to transform the second...

My text defines an elementary permutation as follows: Give 1 <= i < k, let e_i be the element of S_k (where S_k is the set of all permutations of {1,...,k}) defined by setting e_i (j) = j for j not equal to i,i+1; and e_i (i) = i + 1 and e_i (i + 1) = i. It goes on to say that if f is in...

Homework Statement So here's the problem. There is an elevator w/ 5 people equally likely to get off at any of the 7 floor. What is the probability that no two passengers will get off the same floor. Homework Equations The probability of event should be P(E)= number of event...

1. I've only just scrapped through math in high school but recently I have started to take up an interest in the subject. I was listening to a math podcast and they posted a question to be answered the following episode. However, I cannot seem to track that one down and I really need an answer...

Homework Statement P(4,2)+C(5,3) Homework Equations The Attempt at a Solution I think I'm missing something, P(4,2)= 4P2 and C(5,3)=5C3 ?

Homework Statement Find the number of different arrangements of the name "BENNETT TAN" with all the T's separated and all the N's separated. Homework Equations The Attempt at a Solution I have no idea how to start this question. If anyone is so kind to help me. Thank you. I...

Homework Statement If the class contains 7 mechanical, 6 civil and 5 electrical and we require that the 9 individuals who give their presentations on day 1 must include 3 mechanical, 3 civil and 3 electrical, how many different orders of presentation are there for day 1? Homework...