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Arrangements}
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{\noindent{\Large \bf
General Lexicographic Shellability and\\
\rule{0mm}{5mm}Orbit Arrangements}}
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\noindent Dmitry N. Kozlov
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\noindent {\small
Department of Mathematics, Royal Institute of Technology,
S-100 44, Stockholm, Sweden}
\noindent {\small kozlov@math.kth.se}
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\noindent{\small Received May 20, 1996}
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{\small {\it AMS Subject Classification}: 52B30, 05A17, 06A10}
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\noindent {\small {\bf Abstract.} We introduce a new poset property
which we call EC-shellability.
It is more general than the more established 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
$\pl$ of orbit arrangements $\ca_\lambda$ are EC-shellable for
a very large class of partitions $\lambda$. This allows us to compute
the topology of the link and the complement for these arrangements.
In particular, for this class of $\lambda$s, we are able to settle
a conjecture of Bj\"orner [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 $\pl$ is not shellable,
along with other issues scattered throughout the paper.}
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\noindent{\small{\it Keywords}: subspace arrangement, hyperplane arrangement,
poset,
shellability, intersection lattice, homology groups, number partition,
labeling, M\"obius function, $k$-equal arrangement}
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