Almost commuting permutations are near commuting permutations

By Goulnara Arzhantseva, Liviu Paunescu. 2014

76 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b56e67970895b3b61cede52ea31dfc29630a1c69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Hadwin
2. T. Shulman

In Mathematical Physics

1. D. Hadwin
2. T. Shulman

Citations in the corpus

• STABILITY, COHOMOLOGY VANISHING, AND NONAPPROXIMABLE GROUPS (2017, unknown): “This method has failed so far for two reasons: (1) it is very difficult to prove stability directly and (2) even in the case where stability was proven (see, for example, [4] and the references therein as well as [8]), it was proven in a way that completely classifies asymptotic homomorphism and it ”
• Stability of group relations under small Hilbert–Schmidt perturbations (2017, methodology): “Although proving stability for permutations is not the same as for general unitary matrices and requires different techniques, however, as was noticed in [2], it has similar flavor because the normalized Hamming distance can be expressed using the Hilbert-Schmidt distance.”