{"publication_status":"published","date_published":"2020-03-20T00:00:00Z","file_date_updated":"2020-11-20T13:22:21Z","publisher":"Springer Nature","status":"public","external_id":{"isi":["000520918800001"]},"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"day":"20","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297"}],"_id":"7666","abstract":[{"lang":"eng","text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups."}],"citation":{"mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 759–75, doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>.","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. 2020;64:759-775. doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 759–775, 2020."},"license":"https://creativecommons.org/licenses/by/4.0/","date_created":"2020-04-19T22:00:56Z","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Discrete and Computational Geometry","department":[{"_id":"HeEd"}],"quality_controlled":"1","doi":"10.1007/s00454-020-00188-x","acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","date_updated":"2023-08-21T06:13:48Z","ec_funded":1,"has_accepted_license":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"isi":1,"ddc":["510"],"scopus_import":"1","title":"Tri-partitions and bases of an ordered complex","language":[{"iso":"eng"}],"oa_version":"Published Version","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"03","volume":64,"page":"759-775","file":[{"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","date_created":"2020-11-20T13:22:21Z","success":1,"relation":"main_file","file_size":701673,"creator":"dernst","content_type":"application/pdf","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","date_updated":"2020-11-20T13:22:21Z","access_level":"open_access","file_id":"8786"}],"year":"2020","type":"journal_article","oa":1,"article_processing_charge":"Yes (via OA deal)","intvolume":"        64"}