Reconstructing Permutations from Cycle Minors

Abstract

The ith cycle minor of a permutation p of the set {1,2,…,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,…,n} can be reconstructed from its set of cycle minors if and only if n≥6. We then use this to provide an alternate proof of a known result on a related reconstruction problem.