# Questions tagged [group-theory]

Questions on the group-theoretic functionality of Mathematica.

153 questions
Filter by
Sorted by
Tagged with
75 views

### 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 ...
140 views

### 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.
74 views

### How to find a set of generators with the smallest number of elements in a permutation group?

Given a permutation group with many generators ...
158 views

134 views

### Reducing to Irreducible Representations

Group Theory Background / Utilities Suppose I give you a list G of matrices which represent some group, in that the matrices are closed under multiplication. In ...
319 views

### CharacterTable for symmetric groups $S_n$ with large $n$

I am looking for a package to generate character tables for symmetric groups $S_n$. At this moment I am using ...
58 views

### Solving abstract factorization problem with Mathematica

I'm a Mathematica newbie. Given something like: $$(r_0 + r_1 a + r_2 a^2 + r_3 a^5)(r'_0 + r'_1b + r'_2 b^2 + r'_3 b^5) = 1 - a^5 b^5$$ I'd like to determine if there exist $r_i,r'_i$ that solve the ...
103 views

### Packages for study presentation of groups

This question asks if there are tools/packages in Mathematica for the study of presentation of groups, but it is almost 7 years old and an answer suggests to use Combinatorica package which is now ...
251 views

### How Can I Compute The Automorphism Group of a Matroid?

I want to compute the automorphism group of a matroid. This reduces to the following (more general) problem: Suppose I have a list of sets $\{\{b_{11},\dots,b_{1k}\},\dots,\{b_{k1},\dots,b_{kk}\}\}$ ...
76 views

### How to decompose a 5-cycles into a permutationproduct of two 3-cycles?

We know that every 3-cycles can be expressed as the product of two commutations. Cycles[{{1, 2, 3}}] == PermutationProduct[Cycles[{{1, 3}}], Cycles[{{3, 2}}]] In ...
1 vote
29 views

...
195 views

### How to delete duplicate graphics of the same kind?

A054247: Number of n X n binary matrices under action of dihedral group of the square D_4. ...
387 views

### How to correctly enumerate all the schemes of this cube coloring problem?

This problem is the fifth question of 1996 Chinese High School Mathematics League or Chinese Mathematical Olympiad in Senior: Choose several colors from the given six different colors to dye six faces ...
83 views

### How to create a set (of matrices) which will be used as an finite group to minimize a function?

I'm new here so I'm a little lost. I need to minimize a function considering that the minimizing parameter belongs to a preestablished set. It all involves matrices.It's something like this: Where ...
122 views

### Orbits of a set $X$ under the action of cyclic permutation $T$

Let $X$ be a set defined as $$X = \{\{\sigma_1, \dots, \sigma_L\} \;|\; \sigma_i = 0,\dots ,n-1\}.$$ Furthermore, let $T:X\longrightarrow X$ be a cyclic permutation  T\cdot\{\sigma_1, \dots, \...
269 views

### Finding invariant matrix given group elements

I have a question about speeding up / optimising the following calculation. I have a feeling there is a way to rewrite it but I can't quite see what to do. In $d=3$ dimensions, given a set of ...
50 views

### Does Mathematica limit the size of a set of permutation group generators?

I tried to generate general and special linear groups PGL2 and PSL2 over finite fields using straightforward algorithms over finite fields: The generators are permutations defined as the additive ...
132 views

### Finding sequence of group generators that yields group element

Here is my permutation group that acts on lists of length 4, defined in terms of four generators: ...
286 views

### Symmetry unique atom coordinates

One thing I love about Mathematica is how easily I can go from the name of a molecule to estimated coordinates of its atoms, with a command like ...
75 views

### How to compute with Mathematica the space representation of a group for a given point set?

A set of points $P = \{p_1,p_2,\dots\} \subset \mathbb{R}^3$ in 3D is given. A symmetry transformation $S \in \mathbb{R}^{3 \times 3}$ is considered here as a matrix which maps the elements of $P$ to ...
177 views

### How to solve problem 599 of Project-Euler

Problem 599 of the Project-Euler is described as follows: The well-known Rubik's Cube puzzle has many fascinating mathematical properties. The 2×2×2 variant has 8 cubelets with a total of 24 visible ...
158 views

### Calculating Rubiks $2 \times 2 \times 2$ Permutation using Cycles

The help page of PermutationGroup shows a neat example on calculating the permutations of a $3\times 3\times 3$: ...
285 views

### Illustration of Motzkin numbers: how to delete duplicates

The $n$-th Motzkin number is the number of different ways of drawing non-intersecting chords between $n$ points on a circle (not necessarily touching every point by a chord -- see https://en.wikipedia....
426 views

### How to use Mathematica to prove that isotropic materials have only two independent parameters

Posts on related issues can be found from here or here. Index symmetries: A stiffness tensor $C$ is a fourth-order tensor with components $c_{ijkl}$ which maps symmetric second-order tensors into ...
95 views

### Delete duplicates when cycle both position and element

Cycle of position means: {a, b, a, a} and {a, a, b, a} is the same. Cycle of element means: ...
1 vote
65 views

### How to evaluate an expression [closed]

I have a 3-dimensional array of numbers say A. I want to evaluate the following expression. $\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...