A proof that supersymmetric Schur polynomials have SNP is invalid because the stated hook-inequality support set is contradicted by the paper's own example and by symmetry.
Postnikov--Stanley polynomials are Lorentzian
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abstract
Postnikov--Stanley polynomials $D_u^w$ are a generalization of skew dual Schubert polynomials to the setting of arbitrary Weyl groups. We prove that Postnikov--Stanley polynomials are Lorentzian by showing that they are degree polynomials of Richardson varieties. Our result yields an interesting class of Lorentzian polynomials related to the geometry of Richardson varieties, generalizes the result that dual Schubert polynomials are Lorentzian (Huh--Matherne--M\'esz\'aros--St. Dizier 2022), and resolves the conjecture that Postnikov--Stanley polynomials have M-convex support (An--Tung--Zhang 2024).
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Supersymmetric Schur polynomials have saturated Newton polytopes
A proof that supersymmetric Schur polynomials have SNP is invalid because the stated hook-inequality support set is contradicted by the paper's own example and by symmetry.