Inclusion-Exclusion Formulas from Independent Complexes
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- Attali, D. & Edelsbrunner, H. Discrete Comput Geom (2007) 37: 59. doi:10.1007/s00454-006-1274-7
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.