Turns out I actually need to solve a harder problem: Find the permutation so that the arithmetic difference between smallest and largest integer after permutation is minimal.https://twitter.com/oe1cxw/status/1119226244992774144 …
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This smells like a dimension/support reduction problem where permutations lead to a minimal support vector/basis.
What is your linear algebra doing in my combinatorics problem? :) Can you elaborate?
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Example: Smallest integer: 000000001?? Largest integer: 01???????? You want permutations that cause the number of used bits between the '1' with the most weight and '1' with the least weight to be as small as possible. You can then right-shift everything to make the LSB '0's..
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disappear. You're then left with the smallest support. I think you're not there yet; one can probably reduce the max value more by moving more '0's within the data to more significant positions, except for the '1' in the MSB position. No idea if this actually works.
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