论文标题
POSET细分和混合CD索引
Poset subdivisions and the mixed cd-index
论文作者
论文摘要
Cd-index是在非交通变量C和d中以多项式表示的Eulerian Poset的不变性。它决定了另一个不变的H-多项式。在本文中，我们研究了POSETS的相对环境。我们介绍了混合的CD-Index，这是POSET的强烈形式细分的不变性，该分数决定了第二作者与Stapledon一起引入的混合H-聚合式。混合的CD索引是非公共变量C'，d'，c，d和e的多项式，并且是根据karu的局部CD索引来定义的。在这里，使用CD索引的分解定理制成。我们最初是由于Ehrenborg-karu引起的分解定理的证据，将其扩展到强大的正式细分类别。我们还在许多示例中计算了混合的CD索引。
The cd-index is an invariant of Eulerian posets expressed as a polynomial in noncommuting variables c and d. It determines another invariant, the h-polynomial. In this paper, we study the relative setting, that of subdivisions of posets. We introduce the mixed cd-index, an invariant of strong formal subdivisions of posets, which determines the mixed h-polynomial introduced by the second author with Stapledon. The mixed cd-index is a polynomial in noncommuting variables c',d',c,d, and e and is defined in terms of the local cd-index of Karu. Here, use is made of the decomposition theorem for the cd-index. We extend the proof of the decomposition theorem, originally due to Ehrenborg-Karu, to the class of strong formal subdivisions. We also compute the mixed cd-index in a number of examples.
