| dc.contributor.author | Doolittle, Joseph | |
| dc.contributor.author | Katthän, Lukas | |
| dc.contributor.author | Nill, Benjamin | |
| dc.contributor.author | Santos, Francisco | |
| dc.contributor.other | Universidad de Cantabria | es_ES |
| dc.date.accessioned | 2025-03-05T17:22:18Z | |
| dc.date.available | 2025-03-05T17:22:18Z | |
| dc.date.issued | 2025-02 | |
| dc.identifier.issn | 2050-5094 | |
| dc.identifier.other | PID2019-106188GB-I00 | es_ES |
| dc.identifier.other | PID2022-137283NB-C21 | es_ES |
| dc.identifier.uri | https://hdl.handle.net/10902/35891 | |
| dc.description.abstract | An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their dimension: - We introduce cyclotomic simplices and exhaustively compute all the cyclotomic simplices of dimension 10 and volume up to 2³¹. Among them, we find five empty ones of width 11 and none of larger width. - Using circulant matrices of a very specific form, we construct empty simplices of arbitrary dimension d and width growing asymptotically as d/arcsinh(1) ~ 1.1346 d. | es_ES |
| dc.description.sponsorship | Work of F. Santos is supported by grants PID2019-106188GB-I00 and PID2022-137283NB-C21 funded by MCIN/AEI/10.13039/501100011033, by the Einstein Foundation Berlin under grant EVF-2015-230 and by project CLaPPo (21.SI03.64658) of Universidad de Cantabria and Banco Santander. B. Nill has been a PI in the Research Training Group Mathematical Complexity Reduction funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 314838170, GRK 2297 MathCoRe, and is currently funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 539867500. | es_ES |
| dc.format.extent | 24 p. | es_ES |
| dc.language.iso | eng | es_ES |
| dc.publisher | Cambridge University Press | es_ES |
| dc.rights | © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (https://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use. | es_ES |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | * |
| dc.source | Forum of Mathematics, Sigma, 2025, 13, e21 | es_ES |
| dc.title | Empty simplices of large width | es_ES |
| dc.type | info:eu-repo/semantics/article | es_ES |
| dc.relation.publisherVersion | https://doi.org/10.1017/fms.2024.131 | es_ES |
| dc.rights.accessRights | openAccess | es_ES |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-106188GB-I00/ES/COMBINATORIA Y COMPLEJIDAD DE ESTRUCTURAS GEOMETRICAS DISCRETAS/ | es_ES |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-137283NB-C21/ES/COMBINATORIA GEOMETRICA Y SUS APLICACIONES AL ALGEBRA/ | es_ES |
| dc.identifier.DOI | 10.1017/fms.2024.131 | |
| dc.type.version | publishedVersion | es_ES |
Excepto si se señala otra cosa, la licencia del ítem se describe como © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (https://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
