9
votes
Accepted
Enumerating subsets with no triple appearing together more than once
In fact, Wikipedia article on Steiner systems that you linked already provides an answer to your question:
An $S(3,4,n)$ is called a Steiner quadruple system. A necessary and sufficient condition for ...
- 34.3k
4
votes
Accepted
Steiner-like systems on $\omega$
Sure, let $K$ be any countably infinite field and let $P$ be the projective plane (or a higher-dimensional projective space) over $K$. Let $S'$ be the set of lines in $P$ (where a line is regarded as ...
- 73.2k
2
votes
Accepted
From Steiner systems to geometric lattices to matroids
Let $B$ be the subsets of $\{1,2,...,22\}$ of size $4$ which are not contained in any block of $S(3,6,22)$. $B$ satisfies the basis exchange property.
Proof:
Let $X,Y\in B$, $a\in X$. $X \setminus ...
- 9,501
1
vote
List coloring of a graph corresponding to a Steiner triple system
The said graph can be seen as the line graph of a rank three linear hypergraph. Some results on list coloring of this is known here. The list chromatic number of this is bounded above by $n$.
- 2,089
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