正则CW-复形的壳型序与Salvetti复形的无圈匹配
Shelling-type orderings of regular CW-complexes and acyclic matchings of the Salvetti complex
摘要：
出于工作的Salvetti和Settepanella，我们介绍了某些总序的面孔，任何壳正规CW-复杂（称为“壳型序”），可用于明确构建最大的非循环匹配的偏序集的细胞给定的复杂。建立在应用这种方法的经典zonotope壳，我们描述了一类最大的非循环匹配的Salvetti复杂的线性复杂的安排。要做到这一点，我们介绍和研究一个新的组合分层的Salvetti复杂。对于所得到的非循环匹配，我们给出了一个明确的描述的关键细胞，只依赖于所选择的线性扩展的偏序集的区域。总是可以选择线性延伸，使得临界单元可以通过Jewell和Orlik定义的无断路集的双射从布置的腔室明确地构造。我们的方法可以推广到任意定向拟阵。
英文摘要：
Motivated by the work of Salvetti and Settepanella we introduce certain total orderings of the faces of any shellable regular CW-complex (called `shelling-type orderings') that can be used to explicitly construct maximum acyclic matchings of the poset of cells of the given complex. Building on an application of this method to the classical zonotope shellings we describe a class of maximum acyclic matchings for the Salvetti complex of a linear complexified arrangement. To do this, we introduce and study a new combinatorial stratification of the Salvetti complex. For the obtained acyclic matchings we give an explicit description of the critical cells that depends only on the chosen linear extension of the poset of regions. It is always possible to choose the linear extension so that the critical cells can be explicitly constructed from the chambers of the arrangement via the bijection to no-broken-circuit sets defined by Jewell and Orlik. Our method can be generalized to arbitraty oriented matroids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
