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arXiv · 1108.2056

A lexicographic shellability characterization of geometric lattices

Ruth Davidson·Patricia Hersh
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Abstract

Geometric lattices are characterized in this paper as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar paradigm as McNamara's characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,...,n}.

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Ruth Davidson, Patricia Hersh. 2011-08-09. A lexicographic shellability characterization of geometric lattices. https://arxiv.org/abs/1108.2056

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