2 problems

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Sampling-without-replacement upper-bound conjecture for the MS algorithm
Sampling-without-replacement upper-bound conjecture. Analogous upper bounds can be established for the ${\sf MS}$ algorithm when sampling is without replacement.
Conjectureopennoisy-sorting permutation-estimation statistical-learningarXiv posted 2 days ago
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The packing-number growth conjecture for the symmetric group
Let $S_n$ be the symmetric group on $n$ elements, and let $B_{\ell_2}(S_n,r)$ denote the relevant $\ell_2$ -ball in the symmetric group, with packing number determined by the Hammin…
Conjectureopenhigh-dimensional-statistics packing-numbers permutation-estimationarXiv posted 2 days ago

Sampling-without-replacement upper-bound conjecture for the MS algorithm