Séminaire Lotharingien de Combinatoire, B83b (2021), 12 pp.
Tilman Möller
Matroids of Combinatorially Formal Arrangements are not Determined by Their Points and Lines
Abstract.
An arrangement of hyperplanes is called formal, if the relations
between the hyperplanes are generated by relations in codimension
2. Formality is not a combinatorial property, raising the question for
a characterization for combinatorial formality. A sufficient condition
for this is if the underlying matroid has no proper lift with the same
points and lines. We present an example of a matroid with such a lift
but no non-formal realization, thus showing that above condition is
not necessary for combinatorial formality.
Received: November 21, 2019.
Accepted: May 16, 2021.
Final Version: June 10, 2021.
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