Zhong-Xue Zhang

collaborators

3 papers

math.CO2024

The Briggs inequality for partitions and overpartitions

Xin-Bei Liu, Zhong-Xue Zhang

A sequence of ${a_{n}}_{n \geq 0}$ satisfies the Briggs inequality if \begin{align*} a_n^2(a_n^2-a_{n-1}a_{n+1})>a_{n-1}^2(a_{n+1}^2-a_na_{n+2}) \end{align*} holds for any $n \geq 1$ .…

math.CO2024

The Briggs inequality of Boros-Moll sequences

Zhong-Xue Zhang, James Jing Yu Zhao

Briggs conjectured that if a polynomial $a_{0} + a_{1} x + \dots + a_{n} x^{n}$ with real coefficients has only negative zeros, then $$a^2_k(a^2_k - a_{k-1}a_{k+1}) > a^2_{k-1}(a^2_{k+1} - a_ka_{…

math.CO2024

Newton polytopes of dual $k$ -Schur polynomials

Bo Wang, Candice X. T. Zhang, Zhong-Xue Zhang

Rado's theorem about permutahedra and dominance order on partitions reveals that each Schur polynomial is M-convex, or equivalently, it has a saturated Newton polytope and this pol…

The Briggs inequality for partitions and overpartitions

The Briggs inequality of Boros-Moll sequences

Newton polytopes of dual k-Schur polynomials

Newton polytopes of dual $k$ -Schur polynomials