Upper bounds for the v-stability index via integer programming

Determine effective upper bounds, obtained via integer programming techniques, for the v-stability index vstab(I) of a monomial ideal I ⊂ S.

Background

There are known upper bounds for the stabilization index of associated primes astab(I) of monomial ideals using integer programming (e.g., work by L. T. Hoa and others).

The authors pose the analogous problem for the v-stability index vstab(I), seeking comparable bounds derived from integer programming methods.

References

Problem 5.7. Let I ⊂ S be a monomial ideal. Using integer programming tech-

niques, determine good upper bounds for the v-stability index vstab(I) of I.

— Asymptotic behaviour of integer programming and the $\text{v}$-function of a graded filtration  (2403.08435 - Ficarra et al., 2024) in Problem 5.7, Section 5 (Open questions), page 11