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A comment on Show HN: The King Wen Permutation: [52, 10, 2]. Parent comment

Re:Show HN: The King Wen Permutation: [52, 10, 2] by gezhengwen on Monday March 23, 2026 @06:47AM (#47487629)
You are right, zero fixed points does not mean total structural difference. Your counterexample is good. My wording was wrong, I will fix it. What interests me is not the statistical rarity, but that 81% of elements are in one orbit — this means the reordering is highly coupled, not a bunch of small local swaps.
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Re:Show HN: The King Wen Permutation: [52, 10, 2] by mcphage on Monday March 23, 2026 @08:05AM (#47488319)
> What interests me is not the statistical rarity, but that 81% of elements are in one orbit — this means the reordering is highly coupled, not a bunch of small local swaps.

But what is the significance of the reordering being highly coupled?

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Re:Show HN: The King Wen Permutation: [52, 10, 2] by gezhengwen on Monday March 23, 2026 @09:35AM (#47489352)
The observation itself is the value — it tells you the King Wen sequence is not a bunch of small local adjustments, but a holistic rearrangement. But it cannot tell you why King Wen arranged it this way.
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Re:Show HN: The King Wen Permutation: [52, 10, 2] by Bimos on Monday March 23, 2026 @10:14PM (#47497901)
You didn't explain or prove there is a reason for it.
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