Discrete & Computational Geometry

, Volume 37, Issue 1, pp 59–77

Inclusion-Exclusion Formulas from Independent Complexes


DOI: 10.1007/s00454-006-1274-7

Cite this article as:
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 [3], and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.LIS laboratory, Domaine Universitaire, BP 46, 38402Saint Martin d'HeresFrance
  2. 2.Department of Computer Science, Duke UniversityDurham, NC 27708USA

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