DC Field | Value | Language |
dc.contributor.author | Milićević, Luka | en_US |
dc.date.accessioned | 2023-10-16T11:50:28Z | - |
dc.date.available | 2023-10-16T11:50:28Z | - |
dc.date.issued | 2023 | - |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/5188 | - |
dc.description.abstract | Let V be a finite-dimensional vector space over Fp . We say that a multilinear form α:Vk→Fp in k variables is d -approximately symmetric if the partition rank of difference α(x1,…,xk)−α(xπ(1),…,xπ(k)) is at most d for every permutation π∈Symk . In a work concerning the inverse theorem for the Gowers uniformity ‖⋅‖U4 norm in the case of low characteristic, Tidor conjectured that any d -approximately symmetric multilinear form α:Vk→Fp differs from a symmetric multilinear form by a multilinear form of partition rank at most Op,k,d(1) and proved this conjecture in the case of trilinear forms. In this paper, somewhat surprisingly, we show that this conjecture is false. In fact, we show that approximately symmetric forms can be quite far from the symmetric ones, by constructing a multilinear form α:Fn2×Fn2×Fn2×Fn2→F2 which is 3-approximately symmetric, while the difference between α and any symmetric multilinear form is of partition rank at least Ω(3√n) . | en_US |
dc.publisher | Cambridge University Press | en_US |
dc.relation | This work was supported by the Serbian Ministry of Education, Science and Technological Development through Mathematical Institute of the Serbian Academy of Sciences and Arts. | en_US |
dc.relation.ispartof | Combinatorics, Probability and Computing | en_US |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | Multilinear forms | Partition rank | Symmetric group | en_US |
dc.title | Approximately symmetric forms far from being exactly symmetric | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1017/S0963548322000244 | - |
dc.contributor.affiliation | Mathematics | en_US |
dc.contributor.affiliation | Mathematical Institute of the Serbian Academy of Sciences and Arts | - |
dc.relation.firstpage | 299 | - |
dc.relation.lastpage | 315 | - |
dc.relation.issue | 2 | - |
dc.relation.volume | 32 | - |
dc.description.rank | ~M22 | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | Article | - |
crisitem.author.orcid | 0000-0002-1427-7241 | - |