论文标题
非欧洲裔Dehn-Sommerville关系
Non-Eulerian Dehn-Sommerville relations
论文作者
论文摘要
古典dehn-苏默维尔关系断言，欧拉（Eulerian）简单综合体的$ h $ vector是对称的。我们建立了Dehn-Sommerville关系的三个概括：一种用于$ h $ h $ - 纯简单复合物的向量，另一个用于旗帜$ h $ h $ - 平衡的简单复合物和分级posets的向量，而另一个则是带有受限奇异的分级寄生的圆磨$ h $ h $ h $ vextors。在所有这些情况下，我们就“来自链接的错误”表示对称性的任何失败。对于简单的络合物，这进一步扩展了Klee的半欧洲关系。
The classical Dehn--Sommerville relations assert that the $h$-vector of an Eulerian simplicial complex is symmetric. We establish three generalizations of the Dehn--Sommerville relations: one for the $h$-vectors of pure simplicial complexes, another one for the flag $h$-vectors of balanced simplicial complexes and graded posets, and yet another one for the toric $h$-vectors of graded posets with restricted singularities. In all of these cases, we express any failure of symmetry in terms of "errors coming from the links." For simplicial complexes, this further extends Klee's semi-Eulerian relations.
