Inclusion-exclusion formulas from independent complexes

D. Attali, H. Edelsbrunner, Discrete & Computational Geometry 37 (2007) 59–77.

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Abstract
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 [3], and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex.
Publishing Year
Date Published
2007-01-01
Journal Title
Discrete & Computational Geometry
Volume
37
Issue
1
Page
59 - 77
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Attali D, Edelsbrunner H. Inclusion-exclusion formulas from independent complexes. Discrete & Computational Geometry. 2007;37(1):59-77. doi:10.1007/s00454-006-1274-7
Attali, D., & Edelsbrunner, H. (2007). Inclusion-exclusion formulas from independent complexes. Discrete & Computational Geometry, 37(1), 59–77. https://doi.org/10.1007/s00454-006-1274-7
Attali, Dominique, and Herbert Edelsbrunner. “Inclusion-Exclusion Formulas from Independent Complexes.” Discrete & Computational Geometry 37, no. 1 (2007): 59–77. https://doi.org/10.1007/s00454-006-1274-7.
D. Attali and H. Edelsbrunner, “Inclusion-exclusion formulas from independent complexes,” Discrete & Computational Geometry, vol. 37, no. 1, pp. 59–77, 2007.
Attali D, Edelsbrunner H. 2007. Inclusion-exclusion formulas from independent complexes. Discrete & Computational Geometry. 37(1), 59–77.
Attali, Dominique, and Herbert Edelsbrunner. “Inclusion-Exclusion Formulas from Independent Complexes.” Discrete & Computational Geometry, vol. 37, no. 1, Springer, 2007, pp. 59–77, doi:10.1007/s00454-006-1274-7.

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