Permutation Definition and 276 Threads

I can't proove why P inverse = P transpose always! P is the permuation matrix, i.e. a matrix is identity but the rows can be interchanged. Thanks in advance.

Puzzle question... I am developing an interactive combination lock that involves utilizing a total of 9 buttons to open a door. I am wondering how many combinations there are if the answer requires a certain three to be pushed on? I am not sure how to calculate this, but I am trying to...

Hello, I'm interested in seeing some proof of the identities involving the levi civita permutation tensor and and the kroneker delta. I've discovered the utility and efficiency of these identities in deriving the standard vector calculus identities involving div, grad, and curl, but I'm sort of...

So, there's this game called "Tsuro". Pretty neat. The game contains square tiles, each with 4 line segments drawn on it, connecting points along the edges. A little more specifically, each tile has 8 points on the edges, 2 on each side, evenly distributed on each side (IE each point is 1/3...

Sorry I am not used to using the tex code, but will learn and explain in words for now! I am trying to prove that for all distinct x and y in a finite set X, there exists a function f in P(X) (the permutation group) such that f(x)=x' and f(y)=y'. Note: x' and y' are also distinct. I have...

A group of 5 boys and 10 girls is lined up in random order-that is, each of the 15! permutaions is assumed to be equally likely. a) What is the probability that the person in the 4th position is a boy? b) What is the probability that a particular boy is in the 3rd position? i tried to...

The question is: A sequence of length 6 is formed from the digits {0,1,2...9}. If no repetition is allowed, how many of these sequences can be formed if: f) the sum of the first two terms is 7? So i set up my place holders: _ _ _ _ _ _ if the first 2 place holders have a sum of 7...

This is mind boggling. There is an array of 16 squares, arranged in a 4 x 4 grid. A supply of 4 A's, B's, C's, and D's are given. How many distinguishable ways are there of placing each of the letters in a square, if, one letter must appear once in each row and each column? I'm lost...

Hi. I've got problem with this task. We have 5 digit. How many 7-digit numbers can we create that has at least 2 different digit? Jurij

in this page I've encountered this topic (it's a topic from combinatorics, so it's relevant to discrete maths with sets and so on [that's my justification to post it here o:) ), anyway from my point of view the page describes poorly the successor operation: "The resulting sequence of...

How many ways can 2 men and 3 women be seated in a row such that no 2 men are sitting beside each other? Now I have always had a problem with overthinking these kinds of questions. I'll usually write something down but then doubt myself. What I did was simply did 2! * 3!. 3 * 2 * 2 * 1 *...

Hi, I'm having trouble understanding a question, which looks deceptively simple. May be it is. I would like to know how any of you would tackle the following problem? There are N men wearing identical hats in a room. They all take off their hats and place it in the center of the room and...

thare are 8 candidates for three student seats how many different ways can the seats be chosen? With the FCP I get 24 If it is a permutation I get 336 which is right and why? Thanks for the help

Hey thanks again, figured these questions out!

permutation question (math) [urgent] image here please solve this problem for me. the correct answer is c. i put 10!/(4!6!), then i know i am suppose to divide/subtract something, but i don't know what. (i have never done this kind of problem before.)

What's the transformation law for the permutation (or Levi-Civita) symbols?

say you have the alternating group An for some permutation group Sn. If you are given An and then 1 odd permutation, must you be able to generate all of Sn? I tried it for S3 and I multiplied all the even perms in S3 by only 1 element that wasn't in A3 and was able to generate all of S3. Does...

I have a test coming up late next week or early in the week after next. In any case I want to be ready and so I have been practicing problems from the text a lot and just wanted to make sure I am not making any mistakes. If you see an answer that is wrong please let me know so I can try to see...

I was recently writing a program that needed to encode a permutation into a single integer number (an index, from 0 to n! - 1). The program transformed the permutation (f.i., of 5 numbers) into a "series of indexes", in the ranges [0..4], [0..3], [0..2], [0..1], 4 indexes in total (one...

can anyone explain me the technique to decompose a random n-cycle into a bucnh of 2 cycles. Thanks in advance.

Consider these problems: 1. In how many ways can 7 boys be seated around a round table? 2. If seven beads of different colors are put on a ring how many different desighns can be made? 3. I have six books with identical black bindings, 8 with identical red bindings. In how many ways can I...

Hi, Can anyone help me with these permutation/combination questions? Solve the equation for n: 1. nC4 = 35 2. nC4 = 70 It would be really good if I got the answers with full explanations, a.s.a.p. Thanks.

what is the number of elements of order 5 in the permutaion group S7?? so what we're concerned with here is, after decompositon into disjoint cycles the l.c.m of the lengths must be 5. since 5 is a prime, the only possible way we could get 5 as l.c.m would be to fix ANY 2 elements amongst the 7...

Why does (a, b)(b, c) = (a, b, c) and why does (a, b)(c, d) = (a, b, c)(b, c, d). I don't understand how we get that c goes to b, since there is no d in the first cycle. Colleen

I am reading through this paper and one stage has got me stumbled: http://www.cs.umbc.edu/~lomonaco/lecturenotes/9811056.pdf The part I don't understand is 4.2.3 Phase 3 of Stage 2. Extraction of reconciled key on page 17. I'm pretty sure this is purely mathematical stuff, so you don't...

Hello, First I will pose my question: I am not sure what this question is asking. Is this question asking for a subgroup of S5 with that consists of six elements? Any help is appreciated. Thankyou.