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The golden ratio is closely related to the Zeckendorf representation which is one of the simplest examples of a numeration system (other than the usual base-$b$ represenations). As such, it's an ...

There are numerous applications of ultrafilters within ergodic theory/combinatorial number theory. Vitaly Bergelson's article gives a very nice review of these. Among the results presented there are ...

1: Hopes. Let me begin by taking away your hope - that is, disproving the conjectured asymptotic, $|{\mathscr{T}_{n,k}}|/2^{2^n} \to 1$.
I will say that a family $\mathcal{F}$ is $k$-rich if for each ...

These may be controversial, but in my personal experience...
Do not try to use reference managers for managing references. They will get things wrong often enough that you will spend more time ...

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