{"main_file_link":[{"open_access":"1","url":"http://arxiv-export-lb.library.cornell.edu/abs/1810.07462"}],"title":"Halfway to Rota’s basis conjecture","quality_controlled":"1","scopus_import":"1","issue":"21","oa_version":"Preprint","intvolume":"      2020","language":[{"iso":"eng"}],"article_type":"original","year":"2020","publisher":"Oxford University Press","day":"01","date_published":"2020-11-01T00:00:00Z","author":[{"last_name":"Bucić","first_name":"Matija","full_name":"Bucić, Matija"},{"last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"full_name":"Pokrovskiy, Alexey","first_name":"Alexey","last_name":"Pokrovskiy"},{"last_name":"Sudakov","first_name":"Benny","full_name":"Sudakov, Benny"}],"doi":"10.1093/imrn/rnaa004","_id":"9576","publication":"International Mathematics Research Notices","publication_status":"published","abstract":[{"text":"In 1989, Rota made the following conjecture. Given n bases B1,…,Bn in an n-dimensional vector space V⁠, one can always find n disjoint bases of V⁠, each containing exactly one element from each Bi (we call such bases transversal bases). Rota’s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (e.g., the conjecture was recently the subject of the collaborative “Polymath” project). In this paper we prove that one can always find (1/2−o(1))n disjoint transversal bases, improving on the previous best bound of Ω(n/logn)⁠. Our results also apply to the more general setting of matroids.","lang":"eng"}],"volume":2020,"date_updated":"2023-02-23T14:01:30Z","type":"journal_article","extern":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"page":"8007-8026","status":"public","external_id":{"arxiv":["1810.07462"]},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa":1,"article_processing_charge":"No","citation":{"short":"M. Bucić, M.A. Kwan, A. Pokrovskiy, B. Sudakov, International Mathematics Research Notices 2020 (2020) 8007–8026.","ama":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. Halfway to Rota’s basis conjecture. <i>International Mathematics Research Notices</i>. 2020;2020(21):8007-8026. doi:<a href=\"https://doi.org/10.1093/imrn/rnaa004\">10.1093/imrn/rnaa004</a>","mla":"Bucić, Matija, et al. “Halfway to Rota’s Basis Conjecture.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 21, Oxford University Press, 2020, pp. 8007–26, doi:<a href=\"https://doi.org/10.1093/imrn/rnaa004\">10.1093/imrn/rnaa004</a>.","ieee":"M. Bucić, M. A. Kwan, A. Pokrovskiy, and B. Sudakov, “Halfway to Rota’s basis conjecture,” <i>International Mathematics Research Notices</i>, vol. 2020, no. 21. Oxford University Press, pp. 8007–8026, 2020.","chicago":"Bucić, Matija, Matthew Alan Kwan, Alexey Pokrovskiy, and Benny Sudakov. “Halfway to Rota’s Basis Conjecture.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/imrn/rnaa004\">https://doi.org/10.1093/imrn/rnaa004</a>.","ista":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. 2020. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020(21), 8007–8026.","apa":"Bucić, M., Kwan, M. A., Pokrovskiy, A., &#38; Sudakov, B. (2020). Halfway to Rota’s basis conjecture. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnaa004\">https://doi.org/10.1093/imrn/rnaa004</a>"},"date_created":"2021-06-21T08:12:30Z","month":"11"}