The Lorentzian conjecture for normalized Schur P-polynomials

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Let λ\lambda be a strict partition, meaning a decreasing sequence of positive integers, and let Pλ(x1,…,xm)P_\lambda(x_1,\ldots,x_m) be its Schur PP-polynomial. Schur-PP conjecture. The normalized polynomial

N(Pλ(x1,…,xm))\mathrm{N}(P_\lambda(x_1,\ldots,x_m))

is Lorentzian for every strict partition λ\lambda. The source gives computational evidence for small strict partitions and notes M-convexity of the support, but the Lorentzian assertion remains open.

References

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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