论文标题
加权Ehrhart系列和类型-U \ Mathsf {B} $ Macmahon公式的模拟
Weighted Ehrhart series and a type-$\mathsf{B}$ analogue of a formula of MacMahon
论文作者
论文摘要
我们提出了一个欧拉多项式概括的公式，即主要指数和下降统计量的联合分布的产生多项式在一组签名的多项式排列上。它具有$ h^*$ - 某个多面体的多项式的描述。此外，我们将一系列多型家族与（普遍的）欧拉（Eulerian）多项式相关联，类型为$ \ mathsf {a} $和$ \ mathsf {b} $。使用此连接，$ \ mathsf {a} $和$ \ Mathsf {b} $（例如allindromicity and Unimodity）的概述的类型$ \ mathsf {a} $类型的属性反映在关联多工具的某些属性中。我们还提出了关于概括下降多项式和多面体与有色（多键）排列之间的联系的结果。
We present a formula for a generalisation of the Eulerian polynomial, namely the generating polynomial of the joint distribution of major index and descent statistic over the set of signed multiset permutations. It has a description in terms of the $h^*$-polynomial of a certain polytope. Moreover, we associate a family of polytopes to (generalised) Eulerian polynomials of types $\mathsf{A}$ and $\mathsf{B}$. Using this connection, properties of the generalised Eulerian numbers of types $\mathsf{A}$ and $\mathsf{B}$, such as palindromicity and unimodality, are reflected in certain properties of the associated polytope. We also present results on generalising the connection between descent polynomials and polytopes to coloured (multiset) permutations.
