Jakub Konieczny
  • Member for 10 years, 8 months
  • Last seen this week
  • Oxford, United Kingdom
Golden ratio in contemporary mathematics
5 votes

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 ...

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Applications of idempotent ultrafilters
5 votes

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 ...

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Reference request: Examples of research on a set with interesting properties which turned out to be the empty set
3 votes

While Siegel zeros are not currently an example, they will hopefully become one in the future.

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Size of a family of sets of $k$-separated functions over $\{0,1,\ldots,n-1\}$
Accepted answer
3 votes

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 ...

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Taking a theorem as a definition and proving the original definition as a theorem
2 votes

The concept of a Sturmian word admits several equivalent definitions which one can work with, and which are not obviously equivalent.

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Time-saving (technology) tricks for writing papers
2 votes

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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