dc.creator | Adhikari, S. D. | es |
dc.creator | Boza Prieto, Luis | es |
dc.creator | Eliahou, Shalom | es |
dc.creator | Revuelta Marchena, María Pastora | es |
dc.creator | Sanz Domínguez, María Isabel | es |
dc.date.accessioned | 2022-07-29T10:47:26Z | |
dc.date.available | 2022-07-29T10:47:26Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | Adhikari, S.D., Boza Prieto, L., Eliahou, S., Revuelta Marchena, M.P. y Sanz Domínguez, M.I. (2018). Equation-regular sets and the Fox–Kleitman conjecture. Discrete Mathematics, 341 (2), 287-298. | |
dc.identifier.issn | 0012-365X | es |
dc.identifier.uri | https://hdl.handle.net/11441/136014 | |
dc.description.abstract | Given k ≥ 1, the Fox–Kleitman conjecture from 2006 states that there exists a nonzero
integer b such that the 2k-variable linear Diophantine equation
∑k
i=1
(xi − yi) = b
is (2k − 1)-regular. This is best possible, since Fox and Kleitman showed that for all
b ≥ 1, this equation is not 2k-regular. While the conjecture has recently been settled for
all k ≥ 2, here we focus on the case k = 3 and determine the degree of regularity of
the corresponding equation for all b ≥ 1. In particular, this independently confirms the
conjecture for k = 3. We also briefly discuss the case k = 4. | es |
dc.format | application/pdf | es |
dc.format.extent | 12 | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Discrete Mathematics, 341 (2), 287-298. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Partition regularity | es |
dc.subject | Degree of regularity | es |
dc.subject | Monochromatic solution | es |
dc.subject | Discrete derivative | es |
dc.title | Equation-regular sets and the Fox–Kleitman conjecture | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) | es |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0012365X17302984?via%3Dihub | es |
dc.identifier.doi | 10.1016/j.disc.2017.08.040 | es |
dc.contributor.group | Universidad de Sevilla. FQM-164: Matemática Discreta: Teoría de Grafos y Geometría Computacional | es |
dc.contributor.group | Universidad de Sevilla. FQM-240: Invariantes en Teoría de Grafos y Optimización | es |
dc.journaltitle | Discrete Mathematics | es |
dc.publication.volumen | 341 | es |
dc.publication.issue | 2 | es |
dc.publication.initialPage | 287 | es |
dc.publication.endPage | 298 | es |
dc.identifier.sisius | 21358238 | es |