Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [permutations]

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

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

12854 questions
2
votes
2 answers

Basic question on permutations

I'm currently studying multilinear algebra and I felt the need to see just the basics of permutations since it's used to study symmetric and antisymmetric tensors. My doubt was: given some permutation how to find it's sign? I mean, how to find the…
Gold
  • 26,547
2
votes
1 answer

How many 5-man starting line-ups are possible?

In an alternate universe, LA Lakers decided to gather the 5 best guards and 10 best forward/centers in their history. One of the guards is Kobe, and one of the forward/centers is Shaq. How many 5-man starting lineups are possible consists of 2…
X X
  • 733
2
votes
0 answers

How many copies of $S_5$ is there in $S_6$

By simple permutations and by fixing one element say $f(6)=6$,we can get a copy of $S_5$ in $S_6$ . Similarly we can obtain 6 different copies , can I obtain a 7th copy?
Raunak Banerjee
  • 21
2
votes
1 answer

Maximum number of letter swaps required to unscramble an n-letter word.

This must be a simple question, but surprisingly, I can't find an answer by googling. What is the maximum number of letter swaps M(n) required to unscramble an n-letter word? By letter swaps I mean swapping letters at positions i and i+1. The n-th…
user1566515
  • 121
2
votes
1 answer

How many positive integers less than $700$ can be formed from the digits $2, 4, 6, 8, 9$?

a) repetitions are allowed; b) repetitions not allowed My solution: a) There are 3 cases: $3$-digit numbers; $2$-digit numbers; one digit numbers. Case 1: $3\times 5\times5=75$ Case 2: $5\times5=25$ Case 3: $5 \times$ Sum of three cases $=…
Armando W
  • 39
  • 6
2
votes
1 answer

How many permutations $\pi$ of $\{1,2,...,n\}$ are there such that $|\pi (i) - i|\le 1$?

How many permutations $\pi$ of $\{1,2,...,n\}$ are there such that $|\pi (i) - i|\le 1$? How would I go about solving this with a proof and teaching it to a non-math major student?
user61646
  • 403
2
votes
1 answer

Fastest way to find the i-th element of the n-th permutation of a sequence

Let say I have a sequence [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] and I want to retrieve the 4th element of the 1,000,000th permutation of this list. I know how to compute the 1,000,000th permutation of the sequence using the algorithm explained here :…
fbparis
  • 153
  • 4
2
votes
1 answer

Computing a lower bound for permutations where ABCD is equal to its reverse (DCBA)?

Given a set of unique elements, the total number of (unique) permutations is n!. For the purpose of my problem, there's an addition to normal equality rules (ABCD == ABCD): Two permutations are equal if one is the reverse of the other: ABCD ==…
vmorph
  • 479
2
votes
1 answer

What are some easy to understand ways of defining an order among a group of people

One of the most popular techniques employed in a game show to define what order people take turns to play a game is by each person picking a piece of paper with the order of play written on it from an urn. What are some other techniques that are…
Omley
  • 123
  • 3
2
votes
2 answers

Ways in which a mixed double game can be arranged from amongest $5$ married couples

The number of ways in which a mixed double game can be arranged from amongest $5$ married couples if at least one husband and wife play in the same game. My Try:: no. of ways in which least one husband and wife play in the same game = Total - no.…
juantheron
  • 53,015
2
votes
3 answers

no. of subsets which have at least $r+1$ element is

A Set has $2r+1$ elements. Then the no. of subsets which have at least $r+1$ element is My Try:: selecting $r+1$ element from $2r+1$ which is $\displaystyle = \binom{2r+1}{r+1}$ selecting $r+2$ element from $2r+1$ which is $\displaystyle =…
juantheron
  • 53,015
2
votes
2 answers

Arrangement around a Circular table

I Did not Understand Arrangement around a Circular Table (i) If Clockwise and Anticlock order are Different (ii) If Clockwise and Anticlock order are not Different for (1) I Have Understand like that arrangement of letters $A,B,C,D,E$ Arrangement…
juantheron
  • 53,015
2
votes
2 answers

Seating arrangement ( permutation)

So I tried this question but somehow I have a hard time understanding what they ask . The question goes : calculate the number of ways 3 girls and 4 boys can be seated in a row of seven(7) chairs if the arrangement is symmetrical. My attempt I am…
user122343
  • 187
  • 1
  • 10
2
votes
2 answers

How many ascending and descending numbers are between 1000 and 9999?

I'm working on some homework right now, and I've gotten stumped. Here's the question I'm on: How many of the 9000 four-digit integers 1000, 1001, 1002, . . . , 9998, 9999 have four distinct digits that are either increasing (as in 1347 and 6789) or…
Dave
  • 237
2
votes
2 answers

The setwise stabiliser of a finite set is maximal in Sym(N)

0 So I'm reading a paper which assumes the following statement but I would like to be able to prove it. Let $S=Sym(\mathbb{N})$ denote the symmetric group on the set of natural numbers. If $\emptyset\subset A \subset \mathbb{N}$ then: $$S_{A}= \{ q…
user8532
1 2 3
…
69 70