dc.contributor.author
Rué, Juanjo
dc.contributor.author
Spiegel, C.
dc.date.accessioned
2026-01-21T12:44:36Z
dc.date.available
2026-01-21T12:44:36Z
dc.date.issued
2026-03-01
dc.identifier.uri
http://hdl.handle.net/2072/489168
dc.description.abstract
We study an analogue of the Ramsey multiplicity problem for additive structures, in particular establishing the minimum number of monochromatic 3-APs in 3-colorings of F3n as well as obtaining the first non-trivial lower bound for the minimum number of monochromatic 4-APs in 2-colorings of F5n. The former parallels results by Cumings et al. [8] in extremal graph theory and the latter improves upon results of Saad and Wolf [42]. The lower bounds are notably obtained by extending the flag algebra calculus of Razborov [39] to additive structures in vector spaces over finite fields. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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dc.description.sponsorship
We would like to thank Oriol Serra for helpful discussions concerning existing results in the additive setting as well as Pascal Schweitzer for valuable input on the isomorphism problem. This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689) , the grants MTM2017-82166-P, PID2020-113082GBI00, PID2023-147202NB-I00, PCI2024-155080-2 and the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) .
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dc.format.extent
21 p.
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dc.relation.ispartof
Finite Fields and Their Applications
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dc.rights
Attribution 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Combinatorial number theory
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dc.subject.other
Ramsey theory
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dc.subject.other
Arithmetic progressions
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dc.subject.other
Flag algebras
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dc.title
The Rado multiplicity problem in vector spaces over finite fields
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.ffa.2025.102782
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
