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Results tagged with combinatorial-designs
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user 515881
Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
9
votes
Accepted
Is every uniform hyperbolic linear space infinite?
The answer is "No".There exist a finite plane with required property.
First of all, let's rephrase your question. Your uniform linear space is a synonym to a BIBD (balanced incomplete block design) wi …
- 501
5
votes
Accepted
Does every finite affine plane have the doubling property?
There is even stronger claim from which follows your answer.
Claim. Any affine plane obtained from Veblen-Weddenburn projective plane by dropping one line don't have "doubling" property.
Proof of this …
- 501
4
votes
Is every uniform hyperbolic linear space infinite?
First answer was just existence of such space.
After routine computer search in large collection of BIBD collected by Vedran Krcadinac, I have two much smaller, nicer and more uniform examples.
First …
- 501
3
votes
Is every uniform hyperbolic linear space infinite?
Other answer that satisfies your criteria.
It's corrected $\operatorname{BIBD}(175, 7, 1)$ from Handbook of combinatorial designs VI.16.2 chapter. Corrected it is because this example is incorrect in …
- 501
2
votes
Is every uniform hyperbolic linear space infinite?
There is very simple example of hyperbolic $\textrm{BIBD}(91,7,1)$. It's following difference family:
$[0, 8, 29, 51, 54, 61, 63]$
$[0, 11, 16, 17, 31, 35, 58]$
$[0, 13, 26, 39, 52, 65, 78]$
over cy …
- 501
1
vote
Is every uniform hyperbolic linear space infinite?
Obtained very interesting example (actually set of examples, but want to emphacise this one).
It's classical (?) example of maximal $\{2^{m+n} - 2^n + 2^m;2^m\}$-arc in $PG(2,2^n)$ projective plane.
D …
- 501
1
vote
Accepted
A graphic representation of classical unitals on 28 points
Using the answer of Taras Banakh, I have implemented an interactive example using HTML and Javascript. It shows all lines of the unital with random colors. Every line is clickable. After clicking on a …
- 501