Almost commuting permutations are near commuting permutations

摘要

We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to k-tuples of almost commuting permutations, for any given k, and allows restrictions, for instance, to even permutations. (C) 2015 Elsevier Inc. All rights reserved.