All Questions
Tagged with magma combinatorics
9
questions
3
votes
0
answers
213
views
Does the percentage of associative operations on a finite set decrease monotonically towards zero?
In this answer, André Nicolas proves that it is rare for a binary operation on a finite set to be associative, in the following sense: if $A_n$ denotes the number of semigroups that can be defined on ...
- 20.8k
5
votes
1
answer
220
views
The ratio of finitely based magmas to all magmas
Let $n$ be a positive integer. By $S_n$, I denote the set of positive integers from $1$ to $n$. By $F_n$, I denote the cardinality of the set of magmas on $S_n$ which are finitely based, that is, ...
- 21.5k
5
votes
1
answer
173
views
Computing the number of conjugacy-classes in $GL_{n}(\mathbb{F}_{p})$ of elementary abelian p-subgroups by GAP and Magma
I'm trying to compute the number of conjugacy-classes of elementary abelian p-subgroups of rank $2$ in $GL_{n}(\mathbb{F}_{p})$ by GAP and Magma. So I consider the following GAP function:
...
1
vote
1
answer
57
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Notation and terminology for free algebras with one binary operation?
Introduction To Question
Context: Universal Algebra
I
Definition: A $\mathtt{S}$-algebra is an algebra $\langle A, succ, \bullet \rangle, $ with one unary operation and no identities.
Let $\mathsf{S}(...
- 1,642
4
votes
1
answer
55
views
How many different operations can be defined in a finite groupoid with a given property?
Set $B=\left\{ 1, 2, ... 18 \right\}$ is given. How many different operations $*$ can be defined so that $(B,*)$ is a groupoid with a property that $|\left\{i|i*(19-i) \neq i ∧ i*(19-i) \neq (19-i)\...
- 455
0
votes
0
answers
42
views
"Compact" formula for counting all products of $x_1,\ldots,x_n$(in that order)?
So here is the problem (I.1.3 in Grillet's Abstract Algebra)
Let $X$ be a set with a binary operation $\cdot:X \times X \to X,$ where $\cdot(x,y):= xy, \text{ for all } x,y\in X$.
A product $x\in X $...
- 1,575
2
votes
1
answer
439
views
Free magmas and binary trees
The free magma on a set $S$ can be constructed by defining $S_0 = S$, $S_{n+1} := \coprod_{p+q=n} S_p \times S_q$ and then endowing $\coprod_{n \geq 0} S_n$ with the evident magma structure (Bourbaki, ...
- 2,584
1
vote
1
answer
117
views
Find the number of different magmas that have $A$ as its underlying set
I have a problem involving algebraic structures. Any help I can get here would be amazing.
Problem: We have a set $A$, $\text{card} A = n$, $n \in \Bbb N$.
Find the number of different magmas that ...
- 557
5
votes
1
answer
529
views
Number of different magmas up to isomorphism
Let $(M,\circ)$ be a magma over a finite set of order $n$. I tried to count all the possible magmas up to isomorphism, but I just can't get it right. My naive approach was to count all the possible ...
- 3,386