dc.contributor.author
Ortega, M.
dc.contributor.author
Rué, J.
dc.contributor.author
Serra, O.
dc.date.accessioned
2024-07-10T13:01:32Z
dc.date.accessioned
2024-09-19T14:26:10Z
dc.date.available
2024-07-10T13:01:32Z
dc.date.available
2024-09-19T14:26:10Z
dc.date.issued
2024-04-15
dc.identifier.uri
http://hdl.handle.net/2072/537713
dc.description
Article Publicat: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/mtk.12255
dc.description.abstract
We prove that product-free subsets of the free group over a finite alpha-
bet have maximum upper density 1/2 with respect to the natural measure
that assigns total weight one to each set of irreducible words of a given
length. This confirms a conjecture of Leader, Letzter, Narayanan andWal-
ters. In more general terms, we actually prove that strongly k-product-
free sets have maximum upper density 1/k in terms of this measure. The
bounds are tight.
eng
dc.description.sponsorship
We acknowledge the support of the grantsMTM2017-82166-P,PID2020-113082GBI00funded by MICIU/AEI/10.13039/501100011033, and the Severo Ochoa and María de Maeztu Programfor Centers and Units of Excellence in R&D (CEX2020-001084-M). Miquel Ortega also acknowlegdes the support of the FPI grantPRE2021-099120.
dc.relation.ispartof
Mathematika
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Combinatronics
dc.title
Product-free sets in the free group
dc.type
info:eu-repo/semantics/article
dc.type
info:eu-repo/semantics/acceptedVersion
dc.identifier.doi
10.1112/mtk.12255
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
