论文标题
矩形的逆Kazhdan-lusztig多项式
The inverse Kazhdan-Lusztig polynomial of a matroid
论文作者
论文摘要
与Coxeter群体的古典Kazhdan-Lusztig多项式类似，Elias，Proudfoot和Wakefield介绍了Kazhdan-Lusztig多项式的概念。众所周知，经典的Kazhdan-Lusztig多项式和Matroid Kazhdan-Lusztig多项式都可以视为局部有限posets的kazhdan-lusztig-stanley多项式的特殊情况。在Kazhdan-Lusztig-Stanley多项式的框架中，我们研究了Kazhdan-Lusztig-Stanley的倒数，并定义了用于矩阵的逆Kazhdan-Lusztig多项式。我们还计算了这些多项式用于布尔原子体和均匀的基生态学。作为逆Kazhdan-lusztig多项式的意外应用，我们获得了一个新公式，用于计算均匀基质的Kazhdan-Lusztig多项式。类似于Matroid的Kazhdan-lusztig多项式，我们猜想其逆Kazhdan-Lusztig多项式的系数是非单位和对数concave的。
In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups, Elias, Proudfoot and Wakefield introduced the concept of Kazhdan-Lusztig polynomials for matroids. It is known that both the classical Kazhdan-Lusztig polynomials and the matroid Kazhdan-Lusztig polynomials can be considered as special cases of the Kazhdan-Lusztig-Stanley polynomials for locally finite posets. In the framework of Kazhdan-Lusztig-Stanley polynomials, we study the inverse of Kazhdan-Lusztig-Stanley functions and define the inverse Kazhdan-Lusztig polynomials for matroids. We also compute these polynomials for boolean matroids and uniform matroids. As an unexpected application of the inverse Kazhdan-Lusztig polynomials, we obtain a new formula to compute the Kazhdan-Lusztig polynomials for uniform matroids. Similar to the Kazhdan-Lusztig polynomial of a matroid, we conjecture that the coefficients of its inverse Kazhdan-Lusztig polynomial are nonnegative and log-concave.
