Verify the conjectured stretched-exponential factor for Classes 247 and 759

Establish whether the counting sequences for Classes 247 and 759, corresponding respectively to $(\leq,-,\geq)$ and $(\leq,\neq,\geq)$, actually possess the conjectured stretched-exponential factor $\mu_1^{n^{3/8}}$ in their dominant asymptotics.

Background

The asymptotic estimates for Classes 247 and 759 are based on numerical analysis and include factors μ1n3/8\mu_1^{n^{3/8}}, with the associated constants estimated rather than rigorously derived. The paper explicitly labels this factor conjectural and relates it to the analogous conjectured behavior of 1324-avoiding permutations.

A rigorous derivation or disproof of this asymptotic form would clarify whether the observed stretched-exponential behavior is genuine for these two inversion-sequence classes.

References

In particular the (conjectured) $\mu_1{n{3/8}$ term (a so-called ``stretched exponential'') is reminiscent of the conjectured behaviour of 1324-avoiding permutations, see for example .

— Completing the enumeration of inversion sequences avoiding triples of relations  (2512.21943 - Britt et al., 26 Dec 2025) in Section 4, Section 4.2, discussion preceding the open-question statement