标题： 铺砌拟阵的逆Kazhdan-Lusztig多项式的对数凹性 显示英文标题

标题： Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids

摘要： 高和谢（2021）推测，任意拟阵的逆Kazhdan-Lusztig多项式都是对数凹的。 尽管逆Kazhdan-Lusztig多项式可能并不总是只有实根，但我们推测，度数分别为$n$和$(1+t)^n$的逆Kazhdan-Lusztig多项式的Hadamard积只有实根。 利用交错多项式和乘子序列，我们对拟阵铺路验证了这个推测。 这一结果使我们能够通过应用牛顿不等式来确认这些拟阵的对数凹性推测。 显示英文摘要

摘要： Gao and Xie (2021) conjectured that the inverse Kazhdan-Lusztig polynomial of any matroid is log-concave. Although the inverse Kazhdan-Lusztig polynomial may not always have only real roots, we conjecture that the Hadamard product of an inverse Kazhdan-Lusztig polynomial of degree $n$ and $(1+t)^n$ has only real roots. Using interlacing polynomials and multiplier sequences, we confirm this conjecture for paving matroids. This result allows us to confirm the log-concavity conjecture for these matroids by applying Newton's inequalities.