Lorentz and Gale–Ryser theorems on general measure spaces

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Boza, Santiago and Křepela, Martin and Soria, Javier (2022) Lorentz and Gale–Ryser theorems on general measure spaces. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 152 (4). pp. 857-878. ISSN 0308-2105

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Official URL: https://doi.org/10.1017/prm.2021.37



Abstract

Based on the Gale–Ryser theorem [2, 6], for the existence of suitable (0,1) -matrices for different partitions of a natural number, we revisit the classical result of Lorentz [4] regarding the characterization of a plane measurable set, in terms of its cross-sections, and extend it to general measure spaces.


Item Type:Article
Uncontrolled Keywords:Cross sections; Nonincreasing rearrangement; Hardy-Littlewood-Pólya relation.
Subjects:Sciences > Mathematics
ID Code:74560
Deposited On:14 Sep 2022 09:48
Last Modified:14 Sep 2022 14:07

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