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
0
votes
1 answer

Find the circle types with three cycles of a set

This question involves the permutation of the set $N=\{1,2,3,4,5,6,7\}.$ What are the cycle types with exactly three cycles? And, for each of these types, how many cycles are there?
Aarafat Alahi
  • 1
0
votes
1 answer

Conditional Permutations with allowed repeating

Let's say we have four elements A, B, C, and D. How can I calculate number of all possible permutations (order matters) for set of 4, if repetitions are allowed, but it is required to have at least one B and one C element in each set? How can I…
Ωmega
  • 125
0
votes
2 answers

permutation of nothing

$p(n,k)$ $k=0$ $p(n,k)=n!/n!=1$ what 1 means? when There is no choice why there will be 1 situation?
johnny is here
  • 7
0
votes
1 answer

Intuitive and memorable way to see N1/n1!n2! as distinct permutations of N objects with n1 of one type and n2 of other. N = n1+n2

Example Problem: Count the number of distinct ways in which N objects, of which n1 are indistinguishably of one type and n2 of a second type, can be accomodated in a total of N = n1 + n2 ways. Solution argument goes like: 1st place can be occupied…
user701723
  • 83
0
votes
2 answers

How many 3 digit numbers are there such that the sum of its digits $\ge$ 10?

For example,the sum of the digits of the number $139=1+3+9=13$ The smallest $3$ digit number to fulfill this condition is $109$ Essentially,this question is asking "For three whole numbers $x,y,z$ find the number of permutations such that $x+ y+…
Feraminecarts
  • 27
0
votes
0 answers

Permutations in the 15 puzzle

The following numberphile video has me stumped. Why is this Puzzle Impossible? - Numberphile It describes the use of parity in permutations to show that the following sequence is impossible {15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,…
Marky0
  • 101
0
votes
0 answers

Is there general method to calculate the times of swapping adjacent elements required to arrange a set of numbers into another order？

Assume I want to change [1,2,...,n] to anthor order, say [n,n-1,...,2,1]. In the exmaple, I know I can do like this [1,2,...,n] $\rightarrow$ [2,1...,n]$\rightarrow$ [2,3,1,...,n]$\rightarrow \cdots \rightarrow$ [2,...,n,1] $\rightarrow$…
RicknJerry
  • 101
0
votes
1 answer

Is there a name and notation for this modified permutation sequence?

I just into this sequence for a problem I'm working on and wondered if it had a name and a mathematical notation. It's the result of creating permutations with replacement where there's also a null case but they can't all be null. There's also no…
jss367
  • 137
0
votes
1 answer

Finding the number of arrangements in this given scenario

What is the difference between the number of combinations you can make when forming a line with 8 girls and 6 boys where at most 3 of the same gender can only be adjacent to each other to when you arrange them in a round circle with the same…
Willie Taylor
  • 69
0
votes
2 answers

Why such a representation is said to be unique when it's known that disjoint cycles commute?

My question is about the underlined statement of Herstein, Topics in Algebra (2nd Ed.) Why such a representation is said to be unique when it's known that disjoint cycles commute? Also $(1,2,3)(4,5)(6)=(1,2,3)(4,5)$ even though as a representation…
Sriti Mallick
  • 6,137
  • 3
  • 30
  • 64
0
votes
1 answer

Number of unique permutations of letters

Let's say there are 7 available letters: ABCDEFG, and I would like to calculate the number of unique 5 letter combinations that can be made, e.g. AABBE. Double letters are perfectly fine, the only thing is that the order doesn't matter, so AABBA and…
MMB
  • 1
0
votes
1 answer

Rearranging a set with limitations on how far each element can move

Suppose we have a set of elements, which we want to rearrange. However, no elements can be moved more than 1 slot away from its original position (items can also be kept in the same position). For instance, with a 3-element set, $ABC$, there are 3…
Thomas Delaney
  • 1,683
0
votes
1 answer

Permutations problems

a) How many strings of 8 distinct letters can be made from the letters {a,b,c,d,e,f,g,h}? b) How many of the strings you found in (a) do not have any of the elements of {a,b,c} next to each other? The first part (a) is easy, it's just 8!. But I have…
Dom Turner
  • 201
  • 1
  • 7
0
votes
1 answer

Permuation with repeated letters and consecutive letters not same

I have been trying to solve a question on permutation and haven't really been successful. I want to generate all the permutations of a specified length that start with a letter and end with the same,and no two consecutive letters should be the same.…
vanandsh
  • 1
  • 2
0
votes
2 answers

How many different arrangements are possible of the letters of the word CARLGAUSS if no S can be in the middle (5th) position?

What I want to do is to first calculate all the possible permutations of the letters of the given word. Once I do that, I plan to keep an S in the 5th position and calculate possible permutations. But the question is do I have to multiply it by 2…
Redeemer X
  • 5
1 2 3
…
69 70