论文标题
仅具有真实根的连锁枚举，分区晶格和多项式
Chain enumeration, partition lattices and polynomials with only real roots
论文作者
论文摘要
有限poset的链多项式的系数通过其元素数量列举了poset。显示晶格的链多项式及其标准型$ b $类似物仅具有真正的根源。链多项式的实用性是针对所有几何晶格的猜想，并且被证明是由金字塔和棱镜对Cohen--Macaulay Posets保存的。结果，提出了凸面的新家族，其面部晶格具有实用的链多项式。还包括对单纯形边界复合物的第二个重中心细分的面部枚举的应用。
The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type $B$ analogues are shown to have only real roots. The real-rootedness of the chain polynomial is conjectured for all geometric lattices and is shown to be preserved by the pyramid and the prism operations on Cohen--Macaulay posets. As a result, new families of convex polytopes whose face lattices have real-rooted chain polynomials are presented. An application to the face enumeration of the second barycentric subdivision of the boundary complex of the simplex is also included.
