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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

11 votes

How many surjections are there from a set of size n?

This looks like the Stirling numbers of the second kind (up to the $m!$ factor). This and this papers are specifically devoted to the maximal Striling numbers. It seems that for large $n$ the releva …
Andrey Rekalo's user avatar
19 votes

Is there a good argument for why you can't place 4 queens which cover a chessboard?

The number of fundamental arrangements one needs to check to prove there is no solution with 4 queens is about $\frac{1}{8}{64 \choose 4}\sim 10^5$ as Mark Meckes noted in his comment. This number …
Andrey Rekalo's user avatar
2 votes

expected values over binomial distributions

This should have been a comment but I don't have enough reputation points to post comments. The expression for $F(n)$ looks very similar to the Bernstein approximation (or Bernstein polynomial) to t …
Andrey Rekalo's user avatar