| dc.contributor.author | Ortega Sánchez Colomer, Miquel |
| dc.contributor.author | Rué Perna, Juan José |
| dc.contributor.author | Serra Albó, Oriol |
| dc.contributor.other | Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2023-11-02T08:44:42Z |
| dc.date.available | 2023-11-02T08:44:42Z |
| dc.date.issued | 2023 |
| dc.identifier.citation | Ortega, M.; Rue, J.; Serra, O. Product-free sets in the free group. A: European Conference on Combinatorics, Graph Theory and Applications. "Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications: EUROCOMB'23. Prague, August 28 - September 1, 2023". 2023, p. 748-753. ISBN 978-80-280-0344-9. DOI 10.5817/CZ.MUNI.EUROCOMB23-103. |
| dc.identifier.isbn | 978-80-280-0344-9 |
| dc.identifier.uri | http://hdl.handle.net/2117/395672 |
| dc.description.abstract | We prove that product-free sets of the free group over a finite alphabet have max-imum density1/2with respect to the natural measure that assigns total weight oneto each set of irreducible words of a given length. This confirms a conjecture ofLeader, Letzter, Narayanan and Walters. In more general terms, we actually provethat stronglyk-product-free sets have maximum density1/kin terms of the saidmeasure. The bounds are tight. |
| dc.description.sponsorship | We acknowledge the support of the grants MTM2017-82166-P, PID2020-113082GB-I00,and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellencein R&D (CEX2020-001084-M). Miquel Ortega also acknowledges the support of the FPIgrant PRE2021-099120. |
| dc.format.extent | 6 p. |
| dc.language.iso | eng |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| dc.subject.lcsh | Free groups |
| dc.subject.other | Combinatoria |
| dc.subject.other | Combinatoria aditiva |
| dc.title | Product-free sets in the free group |
| dc.type | Conference lecture |
| dc.subject.lemac | Grups lliures |
| dc.contributor.group | Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| dc.identifier.doi | 10.5817/CZ.MUNI.EUROCOMB23-103 |
| dc.description.peerreviewed | Peer Reviewed |
| dc.subject.ams | Classificació AMS::20 Group theory and generalizations |
| dc.relation.publisherversion | https://journals.muni.cz/eurocomb/article/view/35637 |
| dc.rights.access | Open Access |
| local.identifier.drac | 36698035 |
| dc.description.version | Postprint (published version) |
| dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-82166-P/ES/COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA/ |
| dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113082GB-I00/ES/COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES/ |
| local.citation.author | Ortega, M.; Rue, J.; Serra, O. |
| local.citation.contributor | European Conference on Combinatorics, Graph Theory and Applications |
| local.citation.publicationName | Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications: EUROCOMB'23. Prague, August 28 - September 1, 2023 |
| local.citation.startingPage | 748 |
| local.citation.endingPage | 753 |
