All Questions
4
questions
5
votes
2
answers
544
views
Can we sometimes define the parity of a set?
Suppose that ${n\choose k}, {n-1\choose k-1}, \ldots, {n-k+1\choose 1}$ are all even. (This happens for example if $k=2^\alpha-1$ and $n=2k$.) In this case, can we select ${n\choose k}/2$ sets of size ...
- 18.5k
4
votes
2
answers
320
views
Is there an infinite number of combinatorial designs with $r=\lambda^{2}$
A quick look at Ed Spence's page reveals two such examples: (7,3,3) and (16,6,3).
If there is a known classification and/or name by which such designs go, I'd love to know about them too.
EDIT: I ...
- 6,832
1
vote
5
answers
348
views
Pairwise balanced designs with $r=\lambda^{2}$
A while ago I asked how to construct an infinite family of $(v,b,r,k,\lambda)$-designs satisfying $r=\lambda^{2}$ and got very good answers from Yuichiro Fujiwara and Ken W. Smith.
Now I'd like to up ...
- 6,832
1
vote
1
answer
795
views
Known results on cyclic difference sets
Is there any infinite family of $v$ for which all the $(v,k,\lambda)$-cyclic difference sets with $k-\lambda$ a prime power coprime to $v$ have been determined?
A subset $D=\{a_1,\ldots,a_k\}$ of $\...
- 767