eprintid: 1560883 rev_number: 28 eprint_status: archive userid: 608 dir: disk0/01/56/08/83 datestamp: 2017-06-30 12:36:31 lastmod: 2021-03-18 23:37:39 status_changed: 2018-09-19 10:59:29 type: article metadata_visibility: show creators_name: Barany, I creators_name: Csoka, E creators_name: Karolyi, G creators_name: Toth, G title: Block partitions: an extended view ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 divisions: F59 keywords: sequence, block partition, transversal note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: Given a sequence S=(s1,…,sm)∈[0,1]m , a block B of S is a subsequence B=(si,si+1,…,sj) . The size b of a block B is the sum of its elements. It is proved in [1] that for each positive integer n, there is a partition of S into n blocks B1, …, B n with |bi−bj|≤1 for every i, j. In this paper, we consider a generalization of the problem in higher dimensions. date: 2018-06-01 date_type: published publisher: SPRINGER official_url: http://doi.org/10.1007/s10474-018-0802-2 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1299738 doi: 10.1007/s10474-018-0802-2 lyricists_name: Barany, Imre lyricists_id: IBARA89 actors_name: Waragoda Vitharana, Nimal actors_id: NWARR44 actors_role: owner full_text_status: public publication: Acta Mathematica Hungarica volume: 155 number: 1 pagerange: 36-46 pages: 11 issn: 1588-2632 citation: Barany, I; Csoka, E; Karolyi, G; Toth, G; (2018) Block partitions: an extended view. Acta Mathematica Hungarica , 155 (1) pp. 36-46. 10.1007/s10474-018-0802-2 <https://doi.org/10.1007/s10474-018-0802-2>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1560883/1/Barany_1706.06095v1.pdf