Lorentz and Gale–Ryser theorems on general measure spaces
| dc.contributor.author | Boza, Santiago | |
| dc.contributor.author | Křepela, Martin | |
| dc.contributor.author | Soria de Diego, Francisco Javier | |
| dc.date.accessioned | 2023-06-22T10:59:10Z | |
| dc.date.available | 2023-06-22T10:59:10Z | |
| dc.date.issued | 2022-08-09 | |
| dc.description.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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO)/FEDER | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/74560 | |
| dc.identifier.doi | 10.1017/prm.2021.37 | |
| dc.identifier.issn | 0308-2105 | |
| dc.identifier.officialurl | https://doi.org/10.1017/prm.2021.37 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/71974 | |
| dc.issue.number | 4 | |
| dc.journal.title | Proceedings of the Royal Society of Edinburgh: Section A Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 878 | |
| dc.page.initial | 857 | |
| dc.publisher | https://www.cambridge.org/core/ | |
| dc.relation.projectID | MTM2016-75196-P | |
| dc.rights | Atribución 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/es/ | |
| dc.subject.cdu | 51 | |
| dc.subject.keyword | Cross sections | |
| dc.subject.keyword | Nonincreasing rearrangement | |
| dc.subject.keyword | Hardy-Littlewood-Pólya relation. | |
| dc.subject.ucm | Matemáticas (Matemáticas) | |
| dc.subject.unesco | 12 Matemáticas | |
| dc.title | Lorentz and Gale–Ryser theorems on general measure spaces | |
| dc.type | journal article | |
| dc.volume.number | 152 | |
| dcterms.references | [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988. [2] D. Gale, A theorem on flows in networks, Pacific J. Math. 7 (1957), 1073–1082. [3] M. Krause, A simple proof of the Gale-Ryser theorem, Amer. Math. Monthly 103 (1996), 335–337. [4] G. G. Lorentz, A problem on plane measures, Amer. J. Math. 71 (1949), 417–426. [5] J. V. Ryff, Measure preserving transformations and rearrangements, J. Math. Anal. Appl. 31 (1970), 449–458. [6] H. J. Ryser, Combinatorial properties of matrices of zeros and ones, Can. J. Math. 9 (1957), 371–377. [7] G. Sierksma and H. Hoogeveen, Seven criteria for integer sequences being graphic, J. Graph Theory 15 (1991), 223–231. [8] W. Sierpi´nski, Sur les fonctions d’ensemble additives et continues, Fund. Math. 3 (1922), 240–246. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | b2108ca5-2270-4783-9661-46cd65b31fc3 | |
| relation.isAuthorOfPublication.latestForDiscovery | b2108ca5-2270-4783-9661-46cd65b31fc3 |
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