Inclusion-Exclusion Formulas from Independent Complexes
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Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We exhibit abstract simplicial complexes that correspond to minimal inclusion-exclusion formulas. They include the dual complex, as defined in , and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex.
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