Effective weight bounds from monomial expansions

Determine a tractable combinatorial method for bounding the weight of a sequence of homogeneous symmetric functions \((F_n\in\Lambda^{(n)})_n\) when a combinatorial formula for its monomial expansions is available but its Schur expansion is unknown.

Background

The main theorem converts monomial stability into Schur stability but requires an independent finite-weight bound. The paper explains that uniform Schur stability generally implies only monomial stability, not uniform monomial stability, so monomial stability alone does not provide finite weight. An effective combinatorial procedure for extracting weight bounds directly from monomial formulas would therefore make the method applicable in situations where Schur expansions are inaccessible.