The steiner-triple-system tag has no usage guidance.

**4**

votes

**2**answers

260 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 ...

**2**

votes

**1**answer

131 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 ...

**4**

votes

**3**answers

173 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

**1**answer

320 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: ...

**3**

votes

**2**answers

295 views

### Can a partial Steiner triple system be completed?

This is probably well-known... but I am afraid the literature on this subject bewilders me a little bit:
Suppose we have a partial Steiner triple system, whereby I mean a finite set $E$ and a set ...

**7**

votes

**4**answers

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 ...

**0**

votes

**1**answer

295 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

**4**

votes

**1**answer

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 ...

**9**

votes

**1**answer

880 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 ...

**3**

votes

**1**answer

440 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.
...