# Tagged Questions

The tag has no usage guidance.

2answers
285 views

### covering designs of the form $(v,k,2)$

A covering design $(v,k,t)$ is a family of subsets of $[v]$ each having $k$ elements such that given any subset of $[v]$ of $t$ elements it is a subset of one of the sets of the family. A problem is ...
1answer
955 views

### Database of Steiner triple systems

Can anyone point me to an online database of Steiner triple systems? My Google-fu is only getting me to descriptions of the few smallest ones, mostly Google book scans (which are rather useless to ...
1answer
149 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 ...
3answers
180 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 ...
4answers
2k views

### Constructing Steiner Triple Systems Algorithmically

I want to create STS(n) algorithmically. I know there are STS(n)s for $n \cong 1,3 \mod 6$. But it is difficult to actually construct the triples. For STS(7) it is pretty easy and but for larger n I ...
1answer
334 views

1answer
319 views

### Why is a block graph of a Steiner Triple System is a Strongly Regular Graph?

With parameters: srg(v(v-1)/6, 3(v-3)/2, (v-3)/2, 9) Should be straightforward counting which alludes me... Thanks! Shay
1answer
458 views

### Diagonally-cyclic Steiner Latin squares

A Steiner triple system is a decomposition of $K_n$ into $K_3$, such as $S=\{013,026,045,124,156,235,346\}$. Steiner triple systems give rise to a Steiner Latin squares, such as $L$ below. \[L=\left(...
1answer
1k views

### Solving a Diophantine equation related to Algebraic Geometry, Steiner systems and $q$-binomials?

The short version of my question is: 1)For which positive integers $k, n$ is there a solution to the equation $$k(6k+1)=1+q+q^2+\cdots+q^n$$ with $q$ a prime power? 2) For which positive ...