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Equipartition of a Segment

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2023Embargo end date: 01 Jan 2020 Denmark Publisher:Institute for Operations Research and the Management Sciences (INFORMS)Journal:Mathematics of Operations Research, volume 48, pages 194-202 (issn: 0364-765X, eissn: 1526-5471,

Authors: Sergey Avvakumov; Roman Karasev;

doi: 10.1287/moor.2022.1260 , 10.48550/arxiv.2009.09862

arXiv: http://arxiv.org/abs/2009.09862

Equipartition of a Segment

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Abstract

We prove that, for any positive integer m, a segment may be partitioned into m possibly degenerate or empty segments with equal values of a continuous function f evaluated on segments, assuming that f may take positive and negative values, but its value on degenerate or empty segments is zero. Funding: S. Avvakumov’s research was supported by the European Research Council under the European Union’s Seventh Framework Programme [ERC Grant StG 716424–CASe]. R. Karasev’s research was partially supported by the Russian Foundation for Basic Research [Grant 19-01-00169].

Country

Denmark

Related Organizations

University of Copenhagen
Denmark
Moscow Institute of Physics and Technology
Russian Federation
Institute for Information Transmission Problems
Russian Federation
University of Copenhagen
Denmark

Keywords

Mathematics - Metric Geometry, fair partition, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Metric Geometry (math.MG), Mathematics - Algebraic Topology, Combinatorics (math.CO), 91B32, 55M20, 55M35, configuration space

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