Logarithmic concavity of Schur and related polynomials

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.

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2022-06, Vol.375 (6), p.4411-4427
Main Authors: June Huh, Jacob P. Matherne, Karola Mészáros, Avery St. Dizier
Format: Article
Language:English
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Description
Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8606