Questions tagged [permutation]

For questions about the functionality related to permutations in Mathematica.

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votes
3answers
64 views

More general permutation of lists

For some arbitrary $N$, I would like to construct all permutations of lists of length $n \leq N$ such that the sum of each permutation list adds to a value less than or equal to $N$. Specifically, ...
2
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1answer
30 views

$2+2+\dots+2$ cycle conjugation classes of the symmetric group $S_n$

Command GroupElements[SymmetricGroup[4]] gives me all cycles of all conjugation classes. But I'm only interested in the 2+2 class ($2+2$ being one of the integer ...
6
votes
2answers
202 views

Find permutation with highest organization number (OEIS A047838)

EDIT: It turns out I misunderstood the definition of "organization number", so the below is incorrect. However, for every permutation I create with my definition of "organization number", I can show ...
0
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1answer
44 views

How to generate all the combinations with repetition?

I have $K$ variables. Each variable can take any value form a set with $N$ elements. We have $N^K$ possible solutions (permutations with repetition, when at each time slot we can choose among $N$ ...
3
votes
1answer
39 views

The product of two symmetric groups acting on a function

Considering the rational function $$ \small \begin{align*} f&(x_1,x_2,x_3;y_1,y_2,y_3)\\ &=\frac{\left(1-\frac{y_1}{x_1}\right)\left(1-\frac{y_2}{x_1}\right)\left(1-\frac{y_3}{x_1}\right)\...
0
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1answer
25 views

Listing Permutations of Two Elements

Let $S_{k}^{(n)}$ be the set of all possible lists of length $n$ containing exactly $k$-times $\sigma$ and $(n-k)$-times $\Delta$. For instance, $S_{2}^{(4)}=\bigl\{\{\sigma,\sigma,\Delta,\Delta\},\{\...
2
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2answers
69 views

Fixed points free permutations [duplicate]

How to generate a list of fixpoint free permutations of n elements in mathematica?
12
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1answer
401 views

ls Ordering[Ordering[list]] optimal?

Given a list list with unique elements, the task is to replace each element by its position in Sort[list]. For example, ...
1
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0answers
62 views

Sum over cyclic permutation of indices

To define the Schouten bracket I need to be able to sum over a cyclic permutation of the indices: $$ [\Phi,\Xi]_S=\mathfrak S_{i,j,k} \left(\Phi^{is}\partial_s\Xi^{jk}+ \Xi^{is}\partial_s\Phi^{jk}\...
12
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2answers
327 views

Terse Method to Swap Lowest for Highest?

I have built a solution to swap the lowest values with the highest values in a list. With ...
1
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0answers
39 views

Permute using symmetric vs alternating groups

Why does this happen? Permute[{0, 0, 0}, SymmetricGroup[3]] (* {{0, 0, 0}} *) Permute[{0, 0, 0}, AlternatingGroup[3]] (* {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} *)
2
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1answer
48 views

Incorporating Signature with Permute for symmetric groups

Let $$f(x_1, x_2, x_3, x_4) := \frac{x_1^{-3} x_2^{-2} x_3^{-1}}{(1 - x_1^2) (1 -x_1^2 x_2^2) (1 - x_1^2 x_2^2 x_3^2) (1 - x_1^2 x_2^2 x_3^2 x_4^2)}.$$ I am trying to compute $$\sum_{w\in S_4} (-1)^{\...
2
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0answers
28 views

How to iterate over Orbit of PermutationGroup?

Another day, another permutation group question. I'm given a g=PermutationGroup[...], and a list l={1, 3, 3, 2, ...}. I know I ...
7
votes
1answer
636 views

Can we turn this for loop into a more elegant Mathematica code?

I am coding stuff manipulating indirection arrays and I have some code like: ...
4
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2answers
86 views

The set of polynomials under the action by a symmetric group

Let $$f(x_1,x_2,x_3)=\frac{x_1^r x_2^r \left(1-x_1 x_3\right) \left(1-x_2 x_3\right)}{\left(1-\frac{x_2}{x_1}\right) \left(1-\frac{x_3}{x_1}\right)\left(1-\frac{x_3}{x_2}\right)},$$ where $r$ is a ...
1
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1answer
38 views

Combinations of a matrix

I want to compute all combinations of a given matrix. I came up with ...
5
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4answers
347 views

Find permutation index

Firstly I wanted to find all the non-negative integer solutions for the following equation given the value of $k_{max}$ $$ k_1 +k_2 +k_3+k_4 = k_{max} $$ For this I use the following code:- ...
6
votes
1answer
106 views

Generate list of tuples, modulo PermutationGroup

I have a permutation group, e.g. g = PermutationGroup[{Cycles[{{1, 2}}]}] but not necessarily limited to a single generating cycle. What I want is to create a ...
1
vote
1answer
54 views

Is there any functions to extract the combinations of sets [closed]

Suppose I have a function f which is depending on a,b,c (f[a_,b_,c_]). these a, b, c can take two value zero and infinity. How to have a combination of the function f when it takes zero and infinity ...
3
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0answers
20 views

Not too obsolete package extending the built-in functionality of Permutation Groups

Is there a modern package geared to permutation groups? With functions, for instance, for group-isomorphism (either w.r.t. permutation representation & w.r.t. group structure), direct, semidirect ...
2
votes
1answer
30 views

How to specify discrete group through permutation cycles

I would like to define a group of order 12 in Mathematica by giving a list of 12 elements in cycle notation, $$ S = \{(e), (123), (132), (12)(45), (13)(45), (23)(45), (13), (23), (12), (45), (123)(45)...
7
votes
2answers
331 views

How to represent a product of cycles in matrix form?

I have a permutation a in a product of disjoint cycles form as follows $a = {{(1,9,3,7)(2,11,6)(4,8,5,10)}}$ I want to represent it in a matrix form ...
1
vote
1answer
47 views

Generating a new list according to the values of the elements of a list

I want to use the command Permute to arrange the rows of a matrix. What I am looking to do is given a list I want to generate a new list which gives me the positions of the elements of the first list ...
1
vote
0answers
134 views

Sum over multiindex

I would like to calculate a sum over some multi-indices, that follow a specific pattern. $$\sum\limits_{1\le i_1<i_2<...<i_k\le N} A(k,i_1, i_2, ..., i_k).$$ $A$ is a fix expression of the ...
2
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0answers
322 views

How do I iterate through all permutations of a list? [closed]

I need to generate all permutation of a list of integers, but doing so (the list has around 60 elements, is not practical. Is there a way to iterate through all permutations of a list, without first ...
0
votes
1answer
55 views

Given a data set, how to do the following

Please help in executing the following problem in Mathematica: I have the following set:$A=\{1, 2,3,4,5,6,7,8,9,10\}$ (my actual data has more than 10 points). I need to do the following three steps: ...
4
votes
1answer
47 views

How to determine computationally the set of linear independent permutations of a tensor with known symmetries?

I have a tensor $t$ with components $t_{i_1 i_2 \dots i_n}$. The tensor $t$ has some index symmetries $\{s_i\}_{i=1}^m$. Consider now all index permutations $p = \{\{1,2,3,\dots,n\},\{2,1,3,\dots,n\},\...
-1
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1answer
70 views

Given the permutation, permute the indices a function

How can we permute the indices of a function? Like in my case I have the permutation of three indices and I am using this code but it isn't working. I have to permute the indices of a. Thanks in ...
12
votes
4answers
398 views

How to generate all involutive permutations?

Take a finite set $S$ (i.e., a list). An involutive permutation is one that squares to the identity. How can we generate all such permutations efficiently, that is, without generating all permutations ...
1
vote
0answers
44 views

Generating list of binomial outcomes [closed]

As an example, imagine if I have a set of 3 coins and I want to generate a list of possible coin states. I know I can brutishly execute: ...
4
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2answers
225 views

Scramble matrix under some condition

Assume I have a matrix. (mat = Partition[Range@9, 3]) // MatrixForm mat$=\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & ...
2
votes
0answers
63 views

Permutations of times that an element appear in a list [duplicate]

I have a list: lis={{a,b},{b,b},{a,a}} This could be a list of types of something, 3 types: the type {a,b}, the type {b,b} and the type {a,a}.Then, I have ten ...
1
vote
1answer
55 views

Permute a list of elements given a pattern

I have this function f and a pattern pattern = f[h[x]]f[h[y]] where h is a generic ...
1
vote
1answer
168 views

Group table for permutation group

I have got a permutation group: $(\{(e,((1, 4),(2,6),(3,5)),((1, 6),(2,5),(3,4)),((1, 5),(2,4),(3,6)),((1, 3,2),(4,6,5)),((1,2,3),(4,5,6)),((1, 4),(2,5),(3,6)),((1, 3),(4,6)),((2, 3),(5,6)),((1, 2),(...
0
votes
2answers
95 views
0
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1answer
86 views

Sum over permuted and unpermuted indices

I would like to write a code to evaluate the following (up to $N=20$) $\sum_{s_1,...,s_N=\pm 1;s_1 \cdot \cdot \cdot s_N=1}\sum_{\sigma\in S_N}\prod_{i=1}^N x_{\sigma(i)}^{s_i \lambda_i}$ There are ...
2
votes
0answers
35 views

Apply all possible permutations into a function [duplicate]

I need to create a function that returns all possible trebles of integers that sum up to a given number. For example, is n=2 then I need something like this: ...
4
votes
2answers
88 views

Improve quality of my code to generating list

I need to write a function that constructs a set of certain permutations of a list of an even number of entries. Below, you can see my program that gives the correct result. ...
6
votes
3answers
550 views

Programming challenge: restricted Permutations

I need to generate the set of all inequivalent permutations for a collection of objects of the form {symbol, integer}. Here is an example collection from which I ...
5
votes
1answer
880 views

Combinations of two lists of lists

I have two sets set1 = {2, 3, 4, 5}; set2 = {1, 3, 4, 5}; and I make permutations of them: ...
0
votes
0answers
49 views

How to rename the output in operations?

The problem is the following, i have 23 Cycles, every cycle have a name: ...
2
votes
1answer
86 views

Sort list but keeping the number of swaps required

I have a set of lists that I want to put into ordered form, but I need to know how many swaps are required to put them into order - these are indexes for minors of a determinant, so each swap gives a ...
5
votes
3answers
282 views

making sub list from a list

I have a list ...
2
votes
1answer
93 views

Sorting of permutations

I would like to output the list of possible permutations of 4 indices but sorted in a certain way. I know that I can the list of possible permutations with ...
5
votes
3answers
347 views

List of the combinations of more lists via permutations

I would like to generate a list of all the possible combinations of two lists. As for instance, given L=3; list={0,1,2}; I would like to obtain the list {{0,...
2
votes
2answers
94 views

Find all permutations with a condition (part 2) [closed]

This question (21008) asks to find all permutations of {a, b, c} subject to a + b + c = n. The answer was provided by Dr. ...
2
votes
2answers
258 views

Sum over permuted indices

Consider this rank 6 tensor: $g_{ab}g_{cd}g_{ef}$. Now I'd like to have a code to sum over all possible $6!$ permutations of the six indices with some coefficient $f[i]$, where $1 \leq i \leq 720$... ...
3
votes
2answers
137 views

How can I output list of permutation products?

I have A = Permutations[{1, 2, 3, 4}]. And c = Cycles[{{1, 2, 3, 4}}]. And I need to output for all $a \in A: a \cdot с \cdot a^{...
17
votes
5answers
1k views

Delete duplicates from list of lists as if on a necklace

Given a list of lists of integers, all of the same length, I want to regard two elements as equivalent if one is the rotated and/or reflected version of another (that is, if the two lists are the same ...
2
votes
2answers
100 views

All Possibilities to skip up to n numbers between a range of numbers

I want to get every possibility to skip up to n numbers between a range of numbers from 0 to m+n-1, whereby m is a self-chosen number. The length of the list should stay constant and should always ...