Inclusion-exclusion complexes for pseudodisk collections

article Inclusion-exclusion complexes for pseudodisk collections published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Edgar Ramos author 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. Springer1997 eng Discrete & Computational Geometry 0179-537610.1007/PL00009295 173287 - 306 yes Edelsbrunner, H., & Ramos, E. (1997). Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry. Springer. <a href="https://doi.org/10.1007/PL00009295">https://doi.org/10.1007/PL00009295</a> H. Edelsbrunner, E. Ramos, Discrete & Computational Geometry 17 (1997) 287–306. Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for Pseudodisk Collections.” Discrete & Computational Geometry. Springer, 1997. <a href="https://doi.org/10.1007/PL00009295">https://doi.org/10.1007/PL00009295</a>. H. Edelsbrunner and E. Ramos, “Inclusion-exclusion complexes for pseudodisk collections,” Discrete & Computational Geometry, vol. 17, no. 3. Springer, pp. 287–306, 1997. Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for Pseudodisk Collections.” Discrete & Computational Geometry, vol. 17, no. 3, Springer, 1997, pp. 287–306, doi:<a href="https://doi.org/10.1007/PL00009295">10.1007/PL00009295</a>. Edelsbrunner H, Ramos E. Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry. 1997;17(3):287-306. doi:<a href="https://doi.org/10.1007/PL00009295">10.1007/PL00009295</a> Edelsbrunner H, Ramos E. 1997. Inclusion-exclusion complexes for pseudodisk collections. Discrete & Computational Geometry. 17(3), 287–306. 40232018-12-11T12:06:30Z2022-08-18T14:39:39Z