A lexicographic shellability characterization of geometric lattices

Details A lexicographic shellability characterization of geometric lattices A lexicographic shellability characterization of geometric lattices

2011-08-09

arxiv.org/abs/1108.2056v1

Mathematics

Combinatorics

7 pages

Scientific paper

Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. 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}. Geometric lattices arise as the intersection lattices of central hyperplane arrangements and more generally as the lattices of flats for matroids.

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