Author

Yuan Gao

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Preprint Sep 2026

Log-concavity of flat arrangement polynomials

We prove log-concavity for the determinant-weighted external semi-activity polynomials of all real flat arrangements, strengthening their known trapezoidality. In fact, we establish a quadratic coefficient inequality that, in rank at least two, implies power concavity with an explicit rank-dependent exponent. The proof...

Yuan Gao, Tian-Yu Yuan · 0 citations

Preprint Aug 2026

Trapezoidality of flat arrangement polynomials

Fox's conjecture predicts that the absolute values of the coefficients of the Alexander polynomial of an alternating link form a trapezoidal sequence. K\'alm\'an, M\'esz\'aros, and Postnikov gave a new proof of trapezoidality for special alternating links using a polynomial associated with flat vector arrangements. We...

Yuan Gao, Tian-Yu Yuan · 1 citation · ⚡1