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Q: Given the Lehmer Code (https://en.wikipedia.org/wiki/Lehmer_code) of a permutation $\sigma$: $$L(\sigma)=(L(\sigma)_1,\ldots,L(\sigma)_n)\quad\text{where}\quad L(\sigma)_i=\#\{ j>i : \sigma_j<\sigma_i \},$$ what is the closed-form formula for the location of each element $i$, i.e., $\sigma_i$?

I know we can use a decoding algorithm to recover the permutation, but it is unclear to me what can be a closed-form formula.

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    $\begingroup$ Not an answer to your question, but an inspiring paper here. $\endgroup$
    – Jean Marie
    Commented Jun 11 at 7:07

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