Logarithmic concavity of Schur and related polynomials

Huh, June; Matherne, Jacob P.; Mészáros, Karola; Dizier, Avery St.

doi:10.1090/tran/8606

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Logarithmic concavity of Schur and related polynomials

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Matherne, Jacob P.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/tran/8606
(Publisher version)

https://doi.org/10.48550/arXiv.1906.09633
(Preprint)

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Citation

Huh, J., Matherne, J. P., Mészáros, K., & Dizier, A. S. (2022). Logarithmic concavity of Schur and related polynomials. Transactions of the American Mathematical Society, 375(6), 4411-4427. doi:10.1090/tran/8606.

Cite as: https://hdl.handle.net/21.11116/0000-000A-75CA-F

Abstract

We show that normalized Schur polynomials are strongly log-concave. As a
consequence, we obtain Okounkov's log-concavity conjecture for
Littlewood-Richardson coefficients in the special case of Kostka numbers.