论文标题
Stembridge代码和Chow戒指
Stembridge codes and Chow rings
论文作者
论文摘要
众所周知，欧拉（Eulerian）多项式是置换体品种的共同体的希尔伯特系列。我们回答了STEMBRIDGE的一个问题，以查找\ emph {置换表示的几何解释}该协同学带来的。我们的解释涉及$ \ mathfrak {s} _n $ - equivariant bivactiant Bivactiant Bivactiant Bixjectiant of Boolean Matroid的Chow环与STEMBRIDGE引入的代码。标准品种有类似的结果。我们提供了其同时携带的置换表示形式的几何解释。这涉及Braden，Huh，Matherne，Proudfoot和Wang引入的Matroid的增强Chow戒指。在此过程中，我们还获得了增强盘环的一些新结果。
It is well known that the Eulerian polynomial is the Hilbert series of the cohomology of the permutohedral variety. We answer a question of Stembridge on finding a geometric explanation of the \emph{permutation representation} this cohomology carries. Our explanation involves an $\mathfrak{S}_n$-equivariant bijection between a basis for the Chow ring of the Boolean matroid and codes introduced by Stembridge. There are analogous results for the stellohedral variety. We provide a geometric explanation of the permutation representation that its cohomology carries. This involves the augmented Chow ring of a matroid introduced by Braden, Huh, Matherne, Proudfoot and Wang. Along the way, we also obtain some new results on augmented Chow rings.
