All Questions
Tagged with combinatorial-designs hyperbolic-geometry
3
questions
5
votes
5
answers
495
views
Is every uniform hyperbolic linear space infinite?
I start with definitions.
Definition 1. A linear space is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ satisfying three axioms:
(L1) for any distinct ...
- 40.2k
4
votes
3
answers
697
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Does there exist a finite hyperbolic geometry in which every line contains at least 3 points, but not every line contains the same number of points?
It seems to me that the answer should be yes, but my naive attempts to come up with an example have failed.
Just to clarify, by finite hyperbolic geometry I mean a finite set of points and lines such ...
- 1,626
3
votes
0
answers
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Existence of finite 3-dimensional hyperbolic balanced geometry
Together with @TarasBanakh we faced the problem described in the title. Let me start with definitions.
A linear space is a pair $(S,\mathcal L)$ consisting of a set $S$ and a family $\mathcal L$ of ...
- 441