0
votes
1answer
132 views

Prove that $\lambda(v-1) = r(k-1)$

This is to do with balanced incomplete block design. Some homework exercise wants me to prove the relation $$\lambda(v-1) = r(k-1)$$ $v$ is the number of elements in your ground set. $r$ is the ...
5
votes
1answer
124 views

Number of combinations such that each pair of combinations has at most x elements in common?

I am doing research on the sense of smell and have a combinatorics problem: I have 128 different odors (n) and I mix them in mixtures of 10 (r). There are 2.26846154e+14 different mixtures. What I ...
1
vote
1answer
353 views

What algorithm is a good to search a lotto design?

I'm interested what kind of algorithm would be suitable to find a lotto design? I saw that is has been proven that $L(39,7,4,7)=329$. This notation is explained in ...
1
vote
1answer
197 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 ...
-1
votes
1answer
80 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
35 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 ...