### Annals of Combinatorics 1 (1997) 67-90

General Lexicographic Shellability and Orbit Arrangements

Dmitry N. Kozlov

Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden
kozlov@math.kth.se

AMS Subject Classification: 52B30, 05A17, 06A10

Abstract. We introduce a new poset property which we call EC-shellability. It is more general than the more stablished concept of EL-shellability, but it still implies shellability. Because of Theorem 3.10, EC-shellability is entitled to be called general lexicographic shellability.
As an application of our new concept, we prove that intersection lattices Πλ of orbit arrangements ${\cal A}_\lambda$ are EC-shellable for a very large class of partitions λ. This allows us to compute the topology of the link and the complement for these arrangements. In particular, for this class of λs, we are able to settle a conjecture of Björner [B94, Conjecture 13.3.2], stating that the cohomology groups of the complement of the orbit arrangements are torsion-free.
We also present a class of partitions for which Πλ is not shellable, along with other issues scattered throughout the paper.

Keywords: subspace arrangement, hyperplane arrangement, poset, shellability, intersection lattice, homology groups, number partition, labeling, Möbius function, k-equal arrangement

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