Pseudo-ASL analogue of Taylor’s resolution

Develop a pseudo-ASL analogue of Diana Taylor’s complex for monomial ideals, namely a canonical free resolution for standard monomial ideals in monomial pseudo-ASLs.

Background

Taylor’s complex provides a canonical (though generally nonminimal) resolution for monomial ideals in polynomial rings. An analogue for standard monomial ideals in monomial pseudo-ASLs would extend homological tools to this generalized setting and support computation of syzygies and invariants.

References

Is there a pseudo-ASL analogue of Diana Taylor's complex for monomial ideals (see Ex.~17.11 for a more widely-accessible description), but now for standard monomial ideals in a monomial pseudo-ASL?

— Gröbner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors (2510.11212 - Grochow et al., 13 Oct 2025) in Future directions and open questions — Theory and geometry