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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
5
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How to efficiently sample uniformly from the set of $p$-equipartitions of an $n$-set?
Randomly permute $n$ and then divide into blocks of size $n/p$.
6
votes
Accepted
Representations of zero as the sum of integers
This is basically covered in section VII.8.1 of Flajolet and Sedgewick's "Analytic Combinatorics". You're looking at the generating function for bridges in their terminology and the form of the genera …