Forward stability in the 231-avoiding class

Establish that for independent permutations u,v drawn uniformly from the avoidance class Av_n(231), the expected forward stability satisfies E[FS(u,v)] = 2n − 5 + o(1) as n→∞.

Background

The paper proves exact record-set equidistribution for Av_n(132) and Av_n(231), implying identical FS distributions when sampling from these classes. Their experiments suggest both lie in a record-sparse regime with stabilization near 2n minus a constant.

This conjecture provides a concrete leading constant term for Av_n(231), refined beyond the general 2n behavior.

References

Conjecture [Record-sparse regime] As n→∞, the following hold. (a) ($231$-avoiding.) If u,v∼ Unif{Av_n(231)}, then \E{\FS(u,v)} = 2n-5+o(1).

— The record statistic and forward stability of Schubert products  (2604.02964 - Hardt et al., 3 Apr 2026) in Section 7 (Conjectures), Conjecture [Record-sparse regime]