论文标题
稀疏铺路矩阵的Kazhdan-Lusztig多项式的组合公式
A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids
论文作者
论文摘要
我们证明了稀疏的铺路曲线的Kazhdan-Lusztig多项式的阳性，这些矩形几乎是对数的，但几乎是所有矩形的。阳性是从我们使用偏斜的年轻tableaux发现了这些多项式的非常简单的组合公式。这支持了以下猜想：所有矩形的kazhdan-lusztig多项式都具有非阴性系数。在特殊情况下，例如统一的基金会，我们的公式具有很好的组合解释。
We prove the positivity of Kazhdan-Lusztig polynomials for sparse paving matroids, which are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. The positivity follows from a remarkably simple combinatorial formula we discovered for these polynomials using skew young tableaux. This supports the conjecture that Kazhdan-Lusztig polynomials for all matroids have non-negative coeffiecients. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation.
