Reconstructing permutations from cycle minors (Q1010923)

Summary: The \(i\)th cycle minor of a permutation \(p\) of the set \(\{1,2,\dots,n\}\) is the permutation formed by deleting an entry \(i\) from the decomposition of \(p\) into disjoint cycles and reducing each remaining entry larger than \(i\) by 1. In this paper, we show that any permutation of \(\{1,2,\dots,n\}\) can be reconstructed from its set of cycle minors if and only if \(n\geq 6\). We then use this to provide an alternate proof of a known result on a related reconstruction problem.