Shellable nonpure complexes and posets .1.
Shellable nonpure complexes and posets .1.
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DOI：
10.1090/s0002-9947-96-01534-6
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发表时间：
1996-04-01
影响因子：
1.3
通讯作者：
Wachs, ML
中科院分区：
文献类型：
--
作者：
Bjorner, A;Wachs, ML
通过删除纯度的要求（即，所有最大的面具有相同的尺寸）。这种普遍性水平的有用性由来自子空间安排理论的某些例子所暗示。我们发展了非纯可壳性概念的几个基本性质，引入了双指标f-向量和h-向量，并证明了后者在可壳性情形下是非负的。可壳复形的同伦类型为不同维数的球楔，其Stanley-Reisner环允许组合诱导的直和分解，posers的字典序可壳性技术也从纯偏序集（所有极大链的长度相同）推广到一般情况.给出了非纯字典序可壳偏序集的几个例子，如k-相等分格（k-相等子空间排列的交格）和二叉树的Tamari格。这导致简化的计算贝蒂数的k-相等的安排。它还确定了同伦类型的间隔在Tamari格和格的号码分区有序的优势，从而加强了一些已知的Mobius函数formula.The扩展到定期CW复杂的简要讨论，并表明是有关的概念，字典式shellability。
The concept of shellability of complexes is generalized by deleting the requirement of purity (i.e., that all maximal faces have the same dimension). The usefulness of this level of generality uas suggested by certain examples coming from the theory of subspace arrangements. We develop several of the basic properties of the concept of nonpure shellability.Doubly indexed f-vectors and h-vectors are introduced, and the latter are shown to be nonnegative in the shellable case. Shellable complexes have the homotopy type of a wedge of spheres of various dimensions, and their Stanley-Reisner rings admit a combinatorially induced direct sum decomposition.The technique of lexicographic shellability for posers is similarly extended from pure posets (all maximal chains of the same length) to the general case. Several examples of nonpure lexicographically shellable posets are given, such as the k-equal partition lattice (the intersection lattice of the k-equal-subspace arrangement) and the Tamari lattices of binary trees. This leads to simplified computation of Betti numbers for the k-equal arrangement. It also determines the homotopy type of intervals in a Tamari lattice and in the lattice of number partitions ordered by dominance, thus strengthening some known Mobius function formulas.The extension to regular CW complexes is briefly discussed and shown to be related to the concept of lexicographic shellability.