{"_id":"75","abstract":[{"text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.","lang":"eng"}],"status":"public","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"first_name":"Sergey","full_name":"Avvakumov, Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"publisher":"arXiv","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"type":"preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"day":"13","title":"Convex fair partitions into arbitrary number of pieces","oa":1,"year":"2018","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:44:30Z","date_updated":"2023-12-18T10:51:02Z","publication_status":"published","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"external_id":{"arxiv":["1804.03057"]},"date_published":"2018-09-13T00:00:00Z","doi":"10.48550/arXiv.1804.03057","article_processing_charge":"No","ec_funded":1,"citation":{"mla":"Akopyan, Arseniy, et al. <i>Convex Fair Partitions into Arbitrary Number of Pieces</i>. 1804.03057, arXiv, 2018, doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>.","apa":"Akopyan, A., Avvakumov, S., &#38; Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>"},"month":"09","article_number":"1804.03057","oa_version":"Preprint"}