The Lorentzian conjecture for normalized skew Schur polynomials in partition notation

Let λ,μZ0n\lambda,\mu\in\mathbb{Z}_{\geq0}^n be partitions satisfying λiμi\lambda_i\geq\mu_i for every ii, and let sλ/μs_{\lambda/\mu} be the skew Schur polynomial. Skew-Schur conjecture. The normalized polynomial

N(sλ/μ)\mathrm{N}(s_{\lambda/\mu})

is Lorentzian. The source reports computational tests for partitions of bounded size; the general assertion remains open.

Sources & referencesView supporting material

Primary source

June Huh, Jacob P. Matherne, Karola Mészáros and Avery St. Dizier, “Logarithmic concavity of Schur and related polynomials”, arXiv:1906.09633 (2019).

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