ALMOST SOLUTIONS OF EQUATIONS IN PERMUTATIONS

By Lev Yu. Glebsky, Luis Manuel Rivera. 2007

53 citations recorded by the source corpus.

We will say that the permutations $f_1,...,f_n$ are an $\epsilon$-solution of an equation if the normalized Hamming distance between its l.h.p. and r.h.p. is $\leq\epsilon$. We give a sufficient conditions when near to an $\epsilon$-solution exists an exact solution and some examples when there does not exist such a solution.

View Paper: https://www.semanticscholar.org/paper/d68976a6c417397ba7bab82a2f24cabfc373861a

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Citations in the corpus

Stability of group relations under small Hilbert–Schmidt perturbations (2017, background): “The interest to stability questions with respect to the normalized Hilbert-Schmidt norm also has appeared recently in group theory, in the context of sofic and hyperlinear groups ([12], [13], [2]).”
Stability and invariant random subgroups (2018, background): “Specializing to H = {1} in Proposition 8.5, we see that a sofic P- stable group must be residually-finite, as proved by Glebsky and Rivera (Theorem 2 of [13]) and by Arzhantseva and Păunescu (Theorem 7.2(ii) of [3]).”
Almost commuting permutations are near commuting permutations (2014, methodology): “ and, under a slight adaptation, for k-tuples of almost commuting even permutations. Stability results are useful to detect a certain rigidity of the corresponding classes of groups. For instance, in [GR09] it was shown that a soﬁc stable (i.e. w ith a stable system of relator words) group is residu”