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. The theory has applications in the area of the design ...

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7
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3answers
1k views

How do you create projective plane out of a finite field?

I have heard and read unclear mentions of links between projective planes and finite fields. Is it possible to construct a projective plane (or a Steiner system) starting out with a field? Could you, ...
5
votes
1answer
172 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 ...
2
votes
1answer
65 views

unbalancing lights

I'm reading the following notes on unbalancing lights, http://www.cs.berkeley.edu/~sinclair/cs271/n5.pdf. The question i have is regarding the first page. Where it says Consider a square $n ...
1
vote
2answers
57 views

Choosing sets of vectors on a complex sphere

Consider a complex $t$ dimensional unit sphere. Can we have $t$ sets of $2^t$ vectors $v_{ij}\in \Bbb C^t$ on the sphere where $i=1$ to $t$ and $j=1$ to $2^t$ on this with inner products satisfying ...
0
votes
0answers
54 views

How to count minimum rows required for combination of pairs

In another thread, I asked a question whether 75 binary options can be tested just by using 4 rows when arranged using an orthogonal array (i.e. contain all pairwise combinations). 4 is the lower ...