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NON‐EULERIAN DEHN–SOMMERVILLE RELATIONS
Mathematika ( IF 0.8 ) Pub Date : 2021-02-01 , DOI: 10.1112/mtk.12072
Connor Sawaske 1 , Lei Xue 1
Affiliation  

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.

中文翻译:

非欧拉式DEHN–SOMMERVILLE关系

经典的Dehn-Sommerville关系断言,欧拉简单复形的h向量是对称的。我们建立了Dehn-Sommerville关系的三种概括:一种是纯单纯形复杂性的h向量,另一种是平衡单纯形复杂性和分级姿势的标志h-向量,另一种是梯度的复曲面h-向量。奇异度受限的坐姿。在所有这些情况下,我们用“来自链接的错误”表示对称性的任何失败。对于简单复合体,这进一步扩展了Klee的半欧拉关系。
更新日期:2021-02-01
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