{"day":"01","publication_status":"published","page":"59 - 77","status":"public","doi":"10.1007/s00454-006-1274-7","title":"Inclusion-exclusion formulas from independent complexes","publisher":"Springer","publication":"Discrete & Computational Geometry","month":"01","date_updated":"2021-01-12T07:53:36Z","issue":"1","date_created":"2018-12-11T12:06:14Z","_id":"3977","type":"journal_article","abstract":[{"text":"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.","lang":"eng"}],"author":[{"last_name":"Attali","full_name":"Attali, Dominique","first_name":"Dominique"},{"first_name":"Herbert","full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"short":"D. Attali, H. Edelsbrunner, Discrete &#38; Computational Geometry 37 (2007) 59–77.","mla":"Attali, Dominique, and Herbert Edelsbrunner. “Inclusion-Exclusion Formulas from Independent Complexes.” <i>Discrete &#38; Computational Geometry</i>, vol. 37, no. 1, Springer, 2007, pp. 59–77, doi:<a href=\"https://doi.org/10.1007/s00454-006-1274-7\">10.1007/s00454-006-1274-7</a>.","ista":"Attali D, Edelsbrunner H. 2007. Inclusion-exclusion formulas from independent complexes. Discrete &#38; Computational Geometry. 37(1), 59–77.","ieee":"D. Attali and H. Edelsbrunner, “Inclusion-exclusion formulas from independent complexes,” <i>Discrete &#38; Computational Geometry</i>, vol. 37, no. 1. Springer, pp. 59–77, 2007.","ama":"Attali D, Edelsbrunner H. Inclusion-exclusion formulas from independent complexes. <i>Discrete &#38; Computational Geometry</i>. 2007;37(1):59-77. doi:<a href=\"https://doi.org/10.1007/s00454-006-1274-7\">10.1007/s00454-006-1274-7</a>","chicago":"Attali, Dominique, and Herbert Edelsbrunner. “Inclusion-Exclusion Formulas from Independent Complexes.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2007. <a href=\"https://doi.org/10.1007/s00454-006-1274-7\">https://doi.org/10.1007/s00454-006-1274-7</a>.","apa":"Attali, D., &#38; Edelsbrunner, H. (2007). Inclusion-exclusion formulas from independent complexes. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-006-1274-7\">https://doi.org/10.1007/s00454-006-1274-7</a>"},"publist_id":"2152","extern":1,"intvolume":"        37","date_published":"2007-01-01T00:00:00Z","quality_controlled":0,"volume":37,"year":"2007"}