Questions tagged [permutation]
For questions about the functionality related to permutations in Mathematica.
273
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3
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Sort the arguments of a function using replace
I want to sort the arguments of a function f while multiplying with the signature of the permutation, i.e. f is totally antisymmetric function. My idea was something like
...
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1
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99
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Can I improve my code to extract permutation cycles from a (n,2) matrix?
I've written a routine to extract permutation cycles from a (n,2) matrix, each row giving the format $a\to b$ which represents the first two elements in some $k$ cycle. If $a\to a$, it's a $1$-cycle. ...
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Find permutation that satisfies conditions
Suppose you what to find a permutation of integers {1, 2, ..., 13} that satisfy some rules.
Rules can be found in variable rules....
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2
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1
answer
94
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Pattern Matching and Permutations
I am working with some math students on some problems involving permutations. My Mathematica knowledge is limited and I'm hoping to get some help. Two sample problems:
a)how many ways can the ...
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1
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2
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118
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How to determine if two colorings of a graph are the same?
A coloring of a graph $G$ with vertex set $V$ is the partitioning of $V$ into so-called color classes so that no two vertices of the same class are adjacent. A $k$-coloring contains exactly $k$ color ...
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3
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4
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175
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Replacing the heads of an expression in left to right order
I would like to replace the occurrences of the head f in an expression.
The expression only contains two possible heads: f and g.
These heads are applied to exactly two arguments.
Example:
...
- 1,698
2
votes
1
answer
81
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Problem with permutations
For a given binary array like {0, 1, 1, 0,..}, I need to find the shortest permutation, sorting it in standard order ...
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1
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65
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Permute subsystems of a matrix?
Suppose I have a matrix $M$ acts on the space $\mathbb C^4\otimes \mathbb C^2\otimes \mathbb C^4\otimes \mathbb C^3$. Is there a method to permute the 2nd subsystem of $M$ and the 4th subsystem of $M$?...
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9
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614
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Rearrange triple sublists
Given a set of triple lists (all contain element 9!)
tripel = {{5, 10, 9}, {4, 9, 3}, {3, 9, 8}, {4, 5, 9}, {9, 10, 8}}
I would ...
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9
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932
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Shuffling two lists into each other
Given a subset s of Range[n] and two lists a and b, with ...
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1
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84
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Value of a function over permutations of two lists
I want to do the sum (in Ising lattice gauge theory)
...
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2
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178
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Select a subset in the bit-strings with even 1s overlapped - thank you
Model 1
Consider the permutation list of 4-bit-strings:
list = Permutations[{0, 0, 1, 1}, {4}]
which outputs:
{{0, 0, 1, 1}, {0, 1, 0, 1}, {0, 1, 1, 0}, {1, 0, 0, ...
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Thermodynamics of the 2D Ising model
I want to study the thermodynamics of the 2D Nearest Neighbour Ising model (calculate the average energy, susceptibility, etc.). I have the Hamiltonian
$$\mathcal{H} = J\sum_{\langle i j \rangle} s_i ...
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4
votes
4
answers
261
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How to confirm two sets contain the same vectors in any order?
Say if I have two sets of vectors, for example:
$$v_{1}=((0,0,0),(0,1,0),(0,0,1),(1,1,1))$$
$$v_{2}=((0,1,0),(1,1,1),(0,0,0),(0,0,1))$$
I want to find a way of verifying that both $v_{1}$ and $v_{2}$ ...
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1
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1
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93
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Elements of a group that send one element to another
If I have a permutation group, say $S_{10}$, how do I get all the permutations that send the set {1, 2, 3} to {5, 6, 7}? I know ...
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How to list all subgroups of symmetry group S_6?
I learned from https://oeis.org/A005432 that $S_6$ has $1455$ subgroups, how can I list them all in mathematica?
As the comment says, the direct approach cannot solve the problem.
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Implementing symmetry assumptions in FullSimplify
I want to symmetrise a long expression, M, that involves a function of 4 arguments, f[u1,u2,d1,d2], and its products (for ...
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0
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Put together all possible combinations of a set of functions, variables, and operators
Using a set of functions, variables, and operators, I'm trying to assemble all of the possible combinations starting with the shortest combination and ending with the longest combination. For example, ...
0
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1
answer
166
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Summation over permutation: $\sum_{\sigma \in S_N} \mathrm{sgn}(\sigma) \prod_{i=1}^N x_{i+\sigma(i)}$
Let $N$ be a natural number, and $S_N$ be the symmetric group over $\{1, \ldots, N\}$. I want to compute
$$\sum_{\sigma \in S_N} \mathrm{sgn}(\sigma) \prod_{i=1}^N x_{i+\sigma(i)}$$
for small $N$ ...
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4
votes
2
answers
391
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How to generate all permutation matrices for 4 qubits?
In quantum mechanics, a qubit can be understood as a 2 by 1 vector denoted by Dirac notation as $$|0\rangle \equiv \left( \begin{array}{c}
1\\
0\\
\end{array} \right) ,|1\rangle \equiv \left( \...
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1
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207
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Arrange 1-n^2 in n×n grid satisfy products of rows equal to products columns
For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the set of products of rows?
I can find solution for $3\times 3$ ...
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1
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2
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127
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Delete the subsets containing the same $2$ integers present in other subsets
From my previous question, if I consider a list like this:
$\{$$\{$$\{$$1,2,3$$\}$,$\{$$4,5,6$$\}$$\}$,
$\{$$\{$$1,2,4$$\}$,$\{$$3,5,6$$\}$$\}$,
$\{$$\{$$1,2,5$$\}$,$\{$$3,4,6$$\}$$\}$,
$\{$$\{$$1,2,6$...
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Cycle symmetric Sort for arguments of a function. Put trace in canonical order
I need a new Sort for the arguments of TR that maintains cyclicity, TR[a,b,c] = TR[b,c,a] = TR[c,a,b]
cyclicSort[TR[b,a,c]]
TR[a,c,b]
...
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7
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3
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245
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Permutations with subsets not containing the same elements
I would like to define a function of two integer variables $ \{n, k\} $, with $ k | n $, that would print all the possible permutations of the first $ n$ positive integers, such that the subsets of $ ...
- 245
4
votes
2
answers
182
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Generating all possible 2x2 matrices with unique elements from 1 to 4
If I have a set A={1,2,3,4}, how do I generate all 2x2 matrices with different elements chosen from ...
4
votes
2
answers
167
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Finding coefficients that impose symmetry
To simplify the main question below,consider the following random multivariate polynomial :
...
- 5,937
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2
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140
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How to get all necklaces without the full permutations' set?
There are previous posts, such as Delete duplicates from list of lists as if on a necklace,
that give a way to find all necklaces from a set of lists. The methods presented there work well for a small ...
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3
votes
4
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250
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Working with tables: add new level of nested tables
I am trying to obtain all possible combinations of elements in a (long) list
factors = {A, B, C};
getCombinations[factors,n]
For n = 3 factors, it should give
<...
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votes
6
answers
265
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How to efficiently find all element combination including a certain element in the list
I have the following list :
alist={{5, 6, 7}, {7, 6, 8}, {5, 7, 25}, {7, 8, 26}, {7, 26, 25}, {5, 4, 6}, {4, 12, 6}, {6, 12, 13}, {6, 13, 8}}
I want to find all ...
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0
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48
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Arranging 4 identical items in 7 spots [closed]
There are 4 unique items, for the sake of the example call them balls. Each ball is exactly the same, and we need to see how many different ways those 4 balls can fit in those 7 slots.
I am not sure ...
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2
votes
1
answer
145
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Permutations with inequalities constraint
In how many ways can I arrange the first $6$ positive integers such that this inequalities chain will hold?
$a < b > c < d < e > f$
One of these arrangements is $\{5, 6, 1, 2, 4, 3\}$, ...
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1
vote
1
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Permutations of Dataset
I have data with missing values. I need all permutations which follow the two rules: Every year must be represented in each draw; and each draw must contain a minimum of two elements for each year. ...
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3
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343
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Find all sets whose index is divisible by the elements
Suppose I have such a set $S=\{3,4,5,...n+2\}, n\in \mathbb{Z}_{>\, 0} $, $a_n$ is any permutation of $S$ such that $n|a_n$, I want to know how many such $a_n$. The easy but inefficient way to do ...
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KSetPartitions function with fixed points
I'm trying to develop a function that computes some numerators for scattering amplitudes and I need to generate a collection of tree diagrams that contain a set of particles (effectively numbers) <...
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1
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460
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Evaluating Pfaffian
The Pfaffian of an even-dimensional anti-symmetric matrix $A$ is defined as:
$$\mathrm{Pf}[A] = \frac{1}{2^{n}n!}\sum_{\pi\in S_{2n}}(-1)^{\pi}
a_{i_{1}i_{2}}a_{i_{3}i_{4}}\cdots a_{i_{2n-1}i_{2n}...
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1
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130
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Accelerating sum over permutations of matrix elements
I am trying to short-cut the use of a CoefficientArrays call by manually calculating the resulting matrix of coefficients myself (this avoids using symbolic arrays ...
1
vote
2
answers
208
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Generating Lyndon words modulo mirroring operation and substituion
I have two letters A,B. I want to generate all words say up to length 22 with the following properties. There is no "canonical" list so any such list will suffice, though there are many ...
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146
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17
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12
answers
4k
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Fastest way to generate {{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}} from {a,b,c}
What is the fastest way to generate {{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}} from l={a,b,c}? I've tried
...
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votes
1
answer
134
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How to convert a PermutationGroup to a named group
We can convert any built-in named group into PermutationGroup by this code(such as AlternatingGroup[5]):
...
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0
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88
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Find Max Instance Over Permutations
I would like to find the maximum of some objective function over all possible permutations
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453
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Is there a function to generate “subsets��� allowing duplicates?
I allow them to be chosen more than once (e.g. allow {1,1}).
(A subset means every element is chosen once or less)
Also I neglect the order (e.g. ...
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3
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139
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How to find the cycle type vector of a random permutation
Given a random permutation $\pi$ of {1,2,...,n}, I want to produce a list {a1,a2,...,an} of nonnegative integers so that ai is the number of cycles in $\pi$ of length i for each i=1,2,...,n. For ...
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1
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57
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Range permutations, treating given runs of consecutive element as they were identical
Given a positive integer $n$ and a list of disjoint intervals in the form $\{\{i_1,i_1+1,i_1+2,\ldots,i_1+n_1\},\{i_2,i_2+1,i_2+2,\ldots i_2+n_2\},\ldots\}$ all contained in $[1,n]$, I want to ...
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3
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604
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Generating signed permutation matrices
As most people (on here at least) know a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. For the $n \times n$ case there are $...
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1
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153
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A code that returns the partial permutations on {1,2,...,n}
A partial permutation is a bijective partial function. A partial function is a map from a subset of {1,2,...,n} into {1,2,...,n}.
I want a list of the matrix representations of all the partial ...
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246
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Permutations with Repetition
I am working with a function of type
F[a,b,c,d,e,f]
that obeys the following symmetries:
...
- 151
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3
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228
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Permutation avoidance function
It is common for me to see if a permutation of 1,2,...,n, avoids some fixed permutation pattern. For example, the permutation [1,4,2,3,5]
contains the pattern 1,3,2, as the elements [1,4,3] appear in ...
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491
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Generating a list of integers that sums to zero
Given a pair of integers n and k, I want to generate all lists of integers of length n, ...
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127
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Binary permutation list code in Mathematica
Given some natural number $N$, I am interested in the set of all binary permutations of length $N$ (with the intention of storing in lists depending on how many $1$'s appear in each permutation). My ...
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