2
votes
1answer
100 views

Hitting sets (aka covers aka transversals) of Steiner triple systems

Does there exist a constant $c$ so that the lines of every Steiner triple system on $v$ points can be covered by $cv$ points? That is if $D \in STS(v)$ with point set $T=\{1,2,\ldots,v\}$ then ...
3
votes
3answers
127 views

Isomorphism testing in STS(13)

What is the simplest isomorphism invariant which can distinguish between the two non-isomorphic Steiner triple systems on $13$ points? Train structure and cycle structure, as described here, do the ...
-1
votes
1answer
298 views

Number of blocks in a t-(v,k,l) design with empty intersection with a given set U [closed]

Question Given a $t-(v,k,\lambda)$ design $(X,\mathcal{B})$ and a set $U\subset X$ with $|U|=u\leq t$, what is the number of blocks $B\in\mathcal{B}$ such that $B\cap U=\emptyset$? The answer is: ...