### co.combinatorics - Replacing logician-constructive with combinatorist-constructive?

Logicians interpret the word "constructive" in a very well-defined way: they take it to mean, more or less, "computability". Taking constructivity seriously and working in a world where everything must be constructive, leads to intuitionistic logic, which has been a very productive and fascinating subfield of logic.On the other hand, combinatorists use "constructive" in a different sense. They use it to mean "better than brute force". For example, Ramsey's theorem is non-constructive from the POV of a combinatorist, since its proof offers no me...Read more

### co.combinatorics - A puzzle about finding three points $(x,y)$, $(x,z)$ and $(y,z)$ in a subset of a square.

I was asked (by myself) to give a proof of the following seemingly simple geometric statement, but after thinking a little I now suspect it could be less elementary than I thought (or am I being silly?). Does anybody know it, and can give an answer or a reference to it? Of course, I'm quite sure it should fit within a larger theory in combinatorics or in probability, but an elementary answer would be appreciated. Let $S$ be a (say open) subset of a square $[0,1]^2$ with Lebesgue measure $|S|>1/2$. Then, there exists a rectangle with a ver...Read more

### co.combinatorics - Multiplication of (0,1) matrices

is there an obvious lattice path counting interpretation for multiplying n by n (0,1) matrices ?...Read more