DC FieldValueLanguage
dc.contributor.authorMilićević, Lukaen_US
dc.date.accessioned2023-10-16T11:50:28Z-
dc.date.available2023-10-16T11:50:28Z-
dc.date.issued2023-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/5188-
dc.description.abstractLet 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.publisherCambridge University Pressen_US
dc.relationThis 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.ispartofCombinatorics, Probability and Computingen_US
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectMultilinear forms | Partition rank | Symmetric groupen_US
dc.titleApproximately symmetric forms far from being exactly symmetricen_US
dc.typeArticleen_US
dc.identifier.doi10.1017/S0963548322000244-
dc.contributor.affiliationMathematicsen_US
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage299-
dc.relation.lastpage315-
dc.relation.issue2-
dc.relation.volume32-
dc.description.rank~M22-
item.cerifentitytypePublications-
item.grantfulltextopen-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith Fulltext-
crisitem.author.orcid0000-0002-1427-7241-
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