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reorder
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RagnarGrootKoerkamp committed Jun 25, 2024
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Expand Up @@ -162,14 +162,14 @@ always there, ready to be found, but nobody did. Schleimers' original bound
It really feels like this proof has been staring us in the face while we didn't
see it for quite some time. Especially given that it's so simple, and all parts
were hinted at:
- The density of a forward scheme can be evaluated by considering a De Bruijn
sequence of order $w+k$, so looking at an order $w+k$ De Bruijn graph should
be necessary and sufficient.
- Partitioning the De Bruijn graph has been done before, to show a density lower
bound of $1/w$.
- The density of random minimizers for $k=1$ is $2/(w+1)$, which, in hindsight,
/very/ much reads like /at least $2$ samples are needed in every cycle of
length $w+1$./
- The density of a forward scheme can be evaluated by considering a De Bruijn
sequence of order $w+k$, so looking at an order $w+k$ De Bruijn graph should
be necessary and sufficient.

*Story time.* Let me briefly write down how I came up with this for my own fun
:) It's in a very very roundabout way:
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