For questions about Combinatorial design theory, a part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
4
votes
1answer
79 views
A generalization of Kirkman's schoolgirl problem
A friend of mine asked me this question. "I have $3n$ elements, and I want to know which is the maximum number of triplets $(a,b,c)$ so that no two triplets have more than one element in common".
The ...
3
votes
2answers
48 views
Geometric solution to classic committee problem
Most people know the classic committe style problems.
I read this solution to one of the basic version of the committe problem and was impressed, but not sure why it works.
I was hoping someone ...
3
votes
2answers
65 views
Applications of design theory
I have recently started reading up on design theory, with the ultimate purpose of doing some original research in that area. I understand the mathematics fairly well, but am not understanding the ...
1
vote
1answer
12 views
Pairwise balanced designs
Let $X$ be a finite set containing $v$ elements and $\lambda$ be a positive integer. Let $K$ be a set of positive integers. Further let there be a multiset $\mathcal{B}$ containing subsets of $X$ ...
0
votes
1answer
31 views
Show that the complement of a difference set is a difference set
In combinatorics, a $(v,k,\lambda)$ difference set is a subset $D$ of cardinality $k$ of a group $G$ of order $v$ such that every nonidentity element of $G$ can be expressed as a product $d_1d_2^{-1}$ ...
1
vote
1answer
61 views
perfect binary e-error correcting code
let C be a perfect binary e-error correcting code of length n.
assume 0 is a symbol and that 0 vector is a codeword.show that P={1,2,...,n}
together with supports of codewords of weight 2e+1form an ...
4
votes
3answers
52 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 ...
-1
votes
1answer
29 views
Golf Round for a group of $12$
$12$ gentlemen wish to play $7$ rounds of golf. They want to split into $3$ groups of $4$ and play a different group each time with as much variety as possible without playing the same individuals ...
2
votes
0answers
21 views
Question related to designs where t= 2
1)Let D be a 2−(v,k,λ) design with b blocks and r blocks through every point. Let B be any block. How to show that the number of blocks that meet B is at least $k(r−1)^2/[(k−1)(λ−1)+(r−1)]$
2) How to ...
4
votes
1answer
155 views
Finding a system of sets resembling the projective plane
For every natural number $r$ I wish to construct a family of sets $\mathcal{F}$ such that
Every set in $\mathcal{F}$ has cardinality $r$ and is a subset of $\{1,2,\ldots,r^2-r+1\},$
For every ...
9
votes
3answers
250 views
Question about members in sets
Let $A_1,A_2,...,A_n$ be sets with $k$ members in $A_i$ for every $1\le i\le n$. Suppose that the $A_i$ satisfy:
1) $|A_i\cap A_j| = 1$ for all $i\ne j$,
2) $A_1\cap A_2\cdots\cap A_n =\emptyset$.
...
3
votes
2answers
50 views
combinatorics question from the real world
This is a real world scenario - please help. My brain hurts and I can't figure it out on my own.
Suppose I host an event with the following constraints
There will be exactly 5 lectures
There will ...
0
votes
0answers
27 views
Name for a type of combinatorial design?
Let $X$ be a ground set, and consider a collection $\mathscr{S}$ of subsets of $X$, $\mathscr{S} = \{S_1, \dots, S_n\}$.
We would like to find a collection $\mathscr{S}'$ with the property that for ...
