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Results tagged with conjectures
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user 90655
for question related to conjectures.
4
votes
1
answer
193
views
Two questions on "Table problem on $\Bbb S^2$"
The following conjecture is known as "Table problem on $\Bbb S^2$"
Conjecture (Table problem on $\Bbb S^2$): Suppose $x_1, x_2,x_3,x_4 \in\Bbb S^2 \subseteq \Bbb R^3$ are the vertices of a
squar …
- 4,195
1
vote
Status of Hadamard matrix conjecture
According to Wikipedia (last edited on 31 March 2017, at 03:48.) the Hadamard conjecture is open still.
- 4,195
3
votes
1
answer
400
views
Can one find a Jordan curve which has exactly one inscribed rectangle?
In On the number of inscribed squares of a simple closed curve in the plane it is shown that
Theorem: For every positive integer $n$ there is a simple closed curve in the
plane (which can be ta …
- 4,195
2
votes
1
answer
389
views
Has the Total Coloring Conjecture been proved for complete graphs?
I have a question on the Total Coloring Conjecture in graph theory. This conjecture states that
$$\chi^"(G)\leq \Delta +2,$$
where $\Delta$ is the maximum degree of the graph and $\chi^"(G)$ denotes …
- 4,195
2
votes
0
answers
284
views
Does this idea give an algorithm for constructing Hadamard matrices?
Fedor Petrov's answer of my preceding question shows that my question reduces to the famous Hadamard conjecture about Hadamard matrices of order $4k$. So I decided to study this conjecture and I got …
- 4,195
16
votes
2
answers
2k
views
Is the Gromov conjecture still open?
Today I read about Gromov's definition of minimal volume for smooth manifolds.
$$\min {\rm Vol}(M):=\inf_{|K_g|\leq1}\{{\rm Vol}(M,g)\}.$$
Gromov's conjecture states that for every closed simply con …
- 4,195