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Results tagged with combinatorial-designs
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user 61536
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.
11
votes
1
answer
388
views
Does every finite affine plane have the doubling property?
Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms:
Any distinct points $x,y\ …
- 41.9k
5
votes
5
answers
562
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 poi …
- 41.9k
2
votes
2
answers
317
views
A graphic representation of classical unitals on 28 points
I would like to understand the geometry of the classical unitals.
They are block designs containing $q^3+1$ points and whose blocks have cardinality $q+1$, where $q$ is a prime power. For $q=2$ (if I …
- 41.9k