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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 …
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 …
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 …