{"status":"public","day":"03","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"11658"}]},"publication":"Journal of Applied and Computational Topology","date_updated":"2024-10-15T06:45:05Z","article_type":"original","corr_author":"1","publisher":"Springer Nature","has_accepted_license":"1","scopus_import":"1","ec_funded":1,"type":"journal_article","language":[{"iso":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2024).","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>"},"abstract":[{"text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_published":"2024-05-03T00:00:00Z","oa_version":"Published Version","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Wittgenstein Award - Herbert Edelsbrunner"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"year":"2024","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s41468-024-00173-w","main_file_link":[{"url":"https://doi.org/10.1007/s41468-024-00173-w","open_access":"1"}],"department":[{"_id":"HeEd"}],"publication_status":"published","month":"05","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","oa":1,"date_created":"2024-05-12T22:01:03Z","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"_id":"15380","author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"first_name":"Sebastiano","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","quality_controlled":"1"}