and ${\mathrm{Newt}}(G_{h,\lambda})$ have IDP and then consider unimodality of the $h^\ast$-vector of ${\mathrm{Newt}}(s_\lambda)$.

Our main contributions in this paper are as follows. We show that all Newton polytopes that arise from Schur polynomials have IDP, and characterize which of these are reflexive. We present closed-form expressions for the $h^\ast$-vectors of those that are reflexive and show that these vectors are all unimodal. This is a family for which Conjecture \[conj-unimodal\] holds. Further, we consider symmetric Grothendieck polynomials, which are linear combinations of Schur polynomials and can be thought of as their inhomogeneous analogue. We show that all Newton polytopes arising from inflated symmetric Grothendieck polynomials have IDP, and characterize the very few that are reflexive.

**Acknowledgments:** The authors would like to thank Federico Castillo and Semin Yoo for helpful discussions and contributions to the early stages of the project.

This work was completed in part at the 2019 Graduate Research Workshop in Combinatorics, which was supported in part by NSF grant \#1923238, NSA grant \#H98230-18-1-0017, a generous award from the Combinatorics Foundation, and Simons Foundation Collaboration Grants \#426971 (to M. Ferrara) and \#315347 (to J. Martin). Margaret Bayer was partially supported by a University of Kansas General Research Fund grant. 