Inclusion-exclusion complexes for pseudodisk collections

H. Edelsbrunner, E. Ramos, Discrete & Computational Geometry 17 (1997) 287–306.

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Abstract
Let B be a finite pseudodisk collection in the plane. By the principle of inclusion-exclusion, the area or any other measure of the union is [GRAPHICS] We show the existence of a two-dimensional abstract simplicial complex, X subset of or equal to 2(B), so the above relation holds even if X is substituted for 2(B). In addition, X can be embedded in R(2) SO its underlying space is homotopy equivalent to int Boolean OR B, and the frontier of X is isomorphic to the nerve of the set of boundary contributions.
Publishing Year
Date Published
1997-04-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
Supported by the National Science Foundation, under Grant ASC-9200301 and the Alan T. Waterman Award CCR-9118874.
Volume
17
Issue
3
Page
287 - 306
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Edelsbrunner H, Ramos E. Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry. 1997;17(3):287-306. doi:10.1007/PL00009295
Edelsbrunner, H., & Ramos, E. (1997). Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry, 17(3), 287–306. https://doi.org/10.1007/PL00009295
Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for Pseudodisk Collections.” Discrete & Computational Geometry 17, no. 3 (1997): 287–306. https://doi.org/10.1007/PL00009295.
H. Edelsbrunner and E. Ramos, “Inclusion-exclusion complexes for pseudodisk collections,” Discrete & Computational Geometry, vol. 17, no. 3, pp. 287–306, 1997.
Edelsbrunner H, Ramos E. 1997. Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry. 17(3), 287–306.
Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for Pseudodisk Collections.” Discrete & Computational Geometry, vol. 17, no. 3, Springer, 1997, pp. 287–306, doi:10.1007/PL00009295.

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