All Questions
Tagged with combinatorial-designs reference-request
7
questions
3
votes
3
answers
678
views
Orthogonal Latin Square 6*6
I need to make remarks about Tarry's Proof for the nonexistence of 6x6 Latin Squares as part of my final exam for a class I'm in. Problem is, I can't find it ANYWHERE on the internet. I can only find ...
- 39
3
votes
1
answer
125
views
On the half-skew-centrosymmetric Hadamard matrices
Definition 1: A Hadamard matrix is an $n\times n$ matrix $H$ whose entries are either $1$ or $-1$ and whose rows are mutually orthogonal.
Definition 2: A matrix $A$ is half-skew-centrosymmetric if ...
- 264
3
votes
0
answers
51
views
Cliques in Incomplete block designs
I'm interested in inequalities that guarantee the presence of cliques in incomplete block designs. Here's the set-up:
I have an incidence structure $(V, B)$ which is an incomplete block design: $V$ is ...
- 11.1k
2
votes
1
answer
128
views
Distinguishing points by sets of given size
The problem is:
Given a finite set $X$ with size $x$ and let $B$ denote a family of $k$-element subsets of $X$, called blocks. What is the smallest possible number $n$ of blocks such that every ...
- 9,282
1
vote
2
answers
146
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Reference Request: "Resolutions" of $K_n$ for $n$ odd
A resolution (in the combinatorial design sense) of $K_{n}$ is a collection of sets of edges of $K_{n}$ so that within each set of edges, each vertex appears once, and over the entire collection, each ...
- 455
1
vote
0
answers
80
views
Bounds for smallest non-trivial designs
Given $s>t\ge 2$, let $N(s,t)$ be the smallest integer $n>s$ such that there exists an “$(n;s;t;1)$-design” (i.e., a collection of $s$-subsets $e_1,\dots,e_m$ of $[n]:=\{1,\dots,n\}$, such that ...
- 2,874
0
votes
1
answer
157
views
"JigSaw Puzzle" on Set Family
One of my research problem can be reduced to a question of the following form
Given a set family $\mathcal{F}$ of $[n]$ , such that every element of $[n]$ lies in exactly $K$ sets in $\mathcal{F}$, ...
- 344