Questions tagged [abstract-algebra]
Abstract algebra is the study of algebraic structures, including groups, rings, fields, vector spaces, and the like.
74 questions
8
votes
2
answers
220
views
Primitive words
Given a list of values, 1, 2, -1, or -2, we will allow the following simple moves:
Remove adjacent values which are negatives of each other. e.g. ...
- 103k
12
votes
8
answers
834
views
Output the symmetric inverse semigroup
The symmetric inverse semigroup is a very important object in the study of semigroups, for a number of reasons, but most obviously due to the Wagner-Preston theorem. In brief, for any set \$X\$, the ...
- 50.8k
20
votes
6
answers
1k
views
Free Kei Friday
A kei (圭) is an algebraic structure that abstracts the idea of mirror reflections.
The kei is given as a set of mirrors \$X\$ and a closed reflection operation \$(\rhd) : X\times X\rightarrow X\$. We ...
- 103k
7
votes
1
answer
355
views
Solving the high school algebra problem
We learned many identities involving addition, multiplication and exponentiation in highschool, for example:
$$ \begin{aligned}
(a+b)c &= ac + bc \\
(a b)^c &= a^c b^c \\
(a^b)^c &= a^{bc}
...
- 805
8
votes
4
answers
420
views
Determine if two trees are equal in the free quandle
To start we are going to define an "\$\operatorname{FBM}\$" as follows:
Every integer is an \$\operatorname{FBM}\$.
If \$a\$ and \$b\$ are \$\operatorname{FBM}\$s, then \$a \lhd b\$ is an \$...
- 103k
6
votes
2
answers
381
views
Count the symmetries
Find the order (size) of the symmetry group of a finite set of integer points in d-dimensional space.
Input
You will be given the coordinates of a finite set of points in d-dimensional space, in any ...
- 2,072
14
votes
5
answers
539
views
Generate a subgroup of a free group
In group theory, the free group with \$n\$ generators can be obtained by taking \$n\$ distinct symbols (let's call them \$a, b, c ...\$ etc), along with their inverses \$ a^{-1},b^{-1},c^{-1} ...\$ . ...
- 46.2k
16
votes
2
answers
684
views
Construct this point
Given a constructible point \$(x, y) \in \mathbb R^2\$, output the steps required to construct \$(x, y)\$
Constructing a point
Consider the following "construction" of a point \$(\alpha, \...
- 50.8k
8
votes
0
answers
361
views
Solve the word problem*
In this challenge you will receive a list of positive integers \$W\$ called a word, and a square symmetric matrix \$M\$. Your task is to determine if the word can be turned into the empty list by ...
- 103k
14
votes
1
answer
339
views
Construct the Constructability sequence
Consider compass-and-straightedge construction, where you can construct new points from existing ones by examining intersections of straight lines and circles constructed with one of the following two ...
- 50.8k
16
votes
6
answers
1k
views
Detect round trips on a hyperbolic grid
You're driving a car in an infinite city whose blocks are pentagons arranged in the order-4 pentagonal tiling. At each step, you proceed to the next intersection and choose whether to continue left, ...
- 871
12
votes
18
answers
690
views
Normal Subgroups of \$S_4\$
Objective
Given a permutation of 4 distinct items, classify the permutation by the normal subgroup(s) it belongs.
Input/Output Format
You gotta choose the followings as the hyperparameters for your ...
- 7,289
10
votes
20
answers
1k
views
Give the inverse permutation
Task
Given a finite permutation output its inverse.
You may take input and output in any reasonable format equivalent to a list of natural numbers. You may choose to use 0 indexing or 1 indexing. ...
- 103k
9
votes
8
answers
555
views
Count the ways to transform
A rigid transformation of a square array is a mapping from square arrays of a certain size to square arrays of the same size, which rearranges the elements of the array such that the distance to each ...
- 103k
11
votes
8
answers
813
views
Expand a Rubik's Cube Commutator
Background
We will be using a 3x3 cube for this challenge.
Rubik's cubers have their own notation for movements on the cube:
Each of the 6 faces has a clockwise turn notated with a single capital ...
- 11.4k