All Questions
Tagged with covering reference-request
8 questions
0
votes
2
answers
96
views
Isometric path cover number of the 2 dimensional grid graph
I am looking for a proof of the fact that at least $2n/3$ isometric paths (i.e. shortest paths between the end points) are required to cover the vertices of the $n\times n$ grid graph (i.e. Cartesian ...
- 1,305
3
votes
1
answer
239
views
Nerve theorem for locally infinite covers by subcomplexes
Let $Y$ be a simplicial complex and let $\{Y_i\}_{i\in I}$ be a set of subcomplexes of $Y$ such that $\bigcup_{i\in I}Y_i=Y$. Let $\mathcal N$ be the nerve of this covering, and assume that for each ...
- 312
5
votes
2
answers
388
views
How much do these interval collections cover?
As usual any related references are appreciated.
Let $p \lt q$ be distinct primes, and for all such pairs, let $m=pq$ and let $\cal{C}$ be the collection $(m-p,m)$ of open intervals. Does (the union ...
- 13k
1
vote
0
answers
70
views
Covering number of the range of a function
I have come across the need to know a bound on a certain curious quantity: the covering number of the range of a continuous function $f: D \rightarrow \mathbb{R}^n$, where $D \subseteq \mathbb{R}^m$. ...
- 183
8
votes
4
answers
659
views
Normal Covering of a Finite Group
Suppose $G$ is a finite group and $N_1, N_2, \cdots, N_k$ are proper normal subgroups of $G$. The set $\{ N_1, \cdots, N_k\}$ is called a normal cover for $G$, if $G = \cup_{i=1}^kN_i$. I need to the ...
8
votes
2
answers
649
views
How to "lift" a transitive group action on a manifold?
Let $M=G/H$ be a homogeneous manifold, with $G$ connected Lie group. Suppose that $\widetilde{M}$ is a covering of $M$.
QUESTION: is there a general prescription to obtain a Lie group $\widetilde{...
- 2,527
21
votes
1
answer
771
views
Covering a set with geometric progressions
Consider the set $S_n=\{1,2,\cdots ,n\}$. What is the minimum number of distinct geometric progressions that cover $S_n$? Let us call this number $a_n$. I was wondering about this number after doing a ...
- 1,090
5
votes
0
answers
1k
views
N-balls covering n-balls
This question is a follow-on question from:
Covering a unit ball with balls half the radius
The questions are these:
Given an arbitrary dimension d, and a unit n-ball in d-dimensional Euclidean ...
- 151