Forward stability in the coGrassmannian class

Establish that for independent permutations u,v drawn uniformly from the coGrassmannian class CoGr_n, the expected forward stability satisfies E[FS(u,v)] = n + (1/√π)√n + O(1) as n→∞.

Background

CoGrassmannian permutations are inverses of Grassmannian permutations and form a natural structured class in Schubert calculus. The paper determines asymptotics for Grassmannian permutations and conjectures a specific √n correction term for the coGrassmannian class.

This conjecture situates coGrassmannian permutations in the record-dense regime where stabilization is close to n but with a sublinear additive fluctuation.

References

Conjecture [Record-dense regime] As n→∞, the following hold. (b) (CoGrassmannian.) If u,v∼ Unif{CoGr_n}, then \E{\FS(u,v)} = n+\frac{1}{\sqrt{\pi}\sqrt{n}+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-dense regime]