All Questions
7 questions
7
votes
1
answer
445
views
What is known/expected on the co-growth series of the braid group?
The co-growth series of finitely generated group with respect to generating set $S$ is generating function for the number of words of length $n$ which are equal to 1 in the group.
Its studies ...
- 24.9k
8
votes
1
answer
304
views
The growth rate of a commutator set in a non-elementary group
Let $G$ be a non-elementary group generated by a finite set $S$. Here, a group is called non-elementary if it is not virtually abelian. Denote $S^{\le n}:=\{g\in G: |g|_S\le n\}$ for any $n\in \mathbb ...
- 145
6
votes
1
answer
290
views
Does the Shalen-Wagreich lemma holds for non-symmetric generating sets?
Let $G$ be a group and $H$ a subgroup with finite index $d$. Then for any finite generating set $S$ of $G$, does $S^{\le k}$ contain a generating set of $H$ where $k$ is a constant depending only on $...
- 145
11
votes
2
answers
789
views
Knot groups with big number of generators
I start by saying that I am not an expert in this field and I apologize if the question is too elementary.
Let $K$ be a knot in $S^3$. I denote by $\pi_1(K)$ the knot group, which is the fundamental ...
- 674
5
votes
0
answers
163
views
Graphs quasi-isometric to a plane
Suppose that a planar graph $\Gamma$ is quasi-isometric to the Euclidean plane. Is it true that the growth function $g(r)$ of $\Gamma$ with respect to any vertex $o$ (that is $g(r)$ is the number of ...
user6976
34
votes
9
answers
7k
views
Applications of infinite graph theory
Finite graph theory abounds with applications inside mathematics itself, in computer science, and engineering. Therefore, I find it naturally to do research in graph theory and I also clearly see the ...
- 349
32
votes
3
answers
3k
views
Is there a reset sequence?
There is a question someone (I'm hazy as to who) told me years ago. I found it fascinating for a time, but then I forgot about it, and I'm out of touch with any subsequent developments. Can anyone ...
- 25.1k