euler A
For any topological space, the Euler characteristic is the alternating sum of its Betti numbers (a.k.a. the ranks of its homology groups). For a central hyperplane arrangement, the associated topological space is the projectivization of its complement.
The Euler characteristic for the hyperplane arrangements defined by root systems are described by simple formulas.
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Given a flat, this method computes the Euler characteristic of the subarrangement indexed by the flat.
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The Euler characteristic of the empty arrangement is just the Euler characteristic of the ambient projective space. For instance, the Euler characteristic of the complex projective plane is $3$.
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