@article{10902/35891,
year = {2025},
month = {2},
url = {https://hdl.handle.net/10902/35891},
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.},
organization = {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.},
publisher = {Cambridge University Press},
publisher = {Forum of Mathematics, Sigma, 2025, 13, e21},
title = {Empty simplices of large width},
author = {Doolittle, Joseph and Katthän, Lukas and Nill, Benjamin and Santos, Francisco},
}