Inclusion-exclusion formulas from independent complexes

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Inclusion-exclusion formulas from independent complexes
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 [2], and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—Geometrical problems and computations, Computations on discrete structures; G.2.1 [Discrete Mathematics]: Combinatorics—Counting problems General Terms Theory, Algorithms Keywords Combinatorial topology, discrete geometry, dual complexes, balls, spheres, indicator functions
Dominique Attali, Herbert Edelsbrunner
Added 13 Oct 2010
Updated 13 Oct 2010
Type Conference
Year 2005
Authors Dominique Attali, Herbert Edelsbrunner
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