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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.

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Even and odd permutations of 123

$\ D_n = \sum_{i,j,k}^n ε_{ijk}···a_i b_j c_k ··· , $ where $\ ε_{ijk···} $, analogous to the Levi-Civita symbol of Section 2.9, is +1 for even permutations1 (ijk ···) of (123 ···n),−1 for odd permutations, and zero if any index is…
mrateb
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How do I calculate the number of ways I can make up number a from the numbers b and c, with n additions of b and/or c?

Say I have a number a: How do I calculate the number of ways I can make up number a from the numbers b and c, with of n additions of b and/or c? For example: a = 4, b = 1, c = 2, n = 3 If I write it out I get the following valid solutions 1 + 1 +…
J4stM4rt
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Formula to calculate distribution of numbers to be grouped

Firstly.. I'm not a mathematician and I apologise upfront if this question is posted in the wrong area. I have the following scenario. I have a bulk of boxes with Box number (such as box1, box2,box3,box4,...) and Box weight such as (Box1 is 2.5kg,…
Eminem
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Which approach is correct and why and why other is wrong

The question is as follows For a game in which every pair has to play with every other pair than find total number of games played if total players is 8 Method 1 - divide 8 into 4 groups of 2 and than selecting 2 grips out of 4 using…
Harsh jain
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How many ways can 9 people line up for a photographer if..

How many ways can 9 people line up for a photographer if a) there are no restrictions? b) Johnny needs to be in the middle? c) Amy and Peter need to be at the ends, and Johnny is in the middle?
Savannah
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What is the no. of permutations of a given set of objects when repetition is allowed?

Suppose we have a set of 12 alphabets. And we are required to form a 7 letter word using the 12 alphabets. Now, since repetition is allowed, the total no. of arrangements would be $\ 12^7$. The total no. of arrangements without any repetition would…
x80W
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Permutation into chained transpositions?

I know that every permutation can be factored as a product of transpositions. I wonder if every permutation can be factored as product of chained transpositions ? For example [5,1,3,0,4,2] = [(3,2),(2,5),(5,0)] \__/ \__/ And,…
Poor Standard
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Permutations : split in two classes and group?

Let say I have a 'p' items 0 ... p . Next we divide them in two groups picking non overlapping numbers. for example let p=4 and we split in two groups. All possible splits are 0:4, 1:3 and 2:2. Lets take 2:2 split, possible group-permutations are…
sten
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Permutations and Combinations in Circular Arrangement

8 persons sit at a round table with 10 seats so that there is exactly one person between the two empty seats. How many possible arrangements are there? Here's what I have so far: ${10 \choose 1}$ (for choosing the seat of the person to be isolated)…
user705198
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Find $\alpha$ and $\beta$ such that ord($\alpha$) = 3 and ord($\beta$) = 3, and ord($\alpha \beta$) = 10

I'm sure this is a really basic question and I'm missing something elementary but I've not been making any sort of headway with this. So in a previous part to the question I was required to find $\alpha$ and $\beta$ such that ord($\alpha$) = 3 and…
AzurePineapple
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What is the connection between number of permutations and number of subsets?

How many different ways to fill 100 boxes in a line with black or white balls. (One box can only contain one ball at a time.) My attempt : Different ways to fill 1 st box = 2 Different ways to fill 2 nd box = 2 Different ways to fill 3 rd box =…
Angelo Mark
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Product of signs of all permutations of fixed length

$S_n$ is a set of all possible permutations of length $n$ here. I think solving it with decrement is too hard and inversions should be used instead. So, it's obvious that $Id$ has zero inversions and 1->n, 2->n-2,...,n->1 has $ \binom{n}{2}$…
Назар Петровский
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universe sized cube and visualising really large numbers

Lets say you have each Planck length in the observable universe represent a googolxgoogolxgoogol Rubik's cube, and create a cube with a total volume of 4.6 x 10^185 of these cubes, each move on any individual cube counts as one permutation, also you…
Mephistophilus
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Circular permutations such that everyone's nearest neighbours are the same

Suppose we want to find the number of ways to make $n$ people sit in a circle. All the arrangements in which everyone has the same nearest neighbours count as the same arrangement. The total number of arranging $n$ people is $n!$ In any of these…
Ryder Rude
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Permutations with changing number of objects - a sequence with a combination of numeric and alphanumerics

A number sequence generator produces 5 digit codes. I believe that we are getting close to maxing out the codes that it is already issued. I would like to calculate the maximum number of permutations and compare it to the distinct count of…
MrGoodfix
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