Helfgott, Harald Andrés

[["dc.bibliographiccitation.firstpage","611"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Annals of Mathematics"],["dc.bibliographiccitation.lastpage","658"],["dc.bibliographiccitation.volume","179"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Seress, Ákos"],["dc.date.accessioned","2017-09-07T11:54:20Z"],["dc.date.available","2017-09-07T11:54:20Z"],["dc.date.issued","2014"],["dc.description.abstract","Given a finite group G and a set A of generators, the diameter diam(Γ(G,A)) of the Cayley graph Γ(G,A) is the smallest ℓ such that every element of G can be expressed as a word of length at most ℓ in A∪A−1. We are concerned with bounding diam(G):=maxAdiam(Γ(G,A)). It has long been conjectured that the diameter of the symmetric group of degree n is polynomially bounded in n, but the best previously known upper bound was exponential in nlogn−−−−−√. We give a quasipolynomial upper bound, namely, diam(G)=exp(O((logn)4loglogn))=exp((loglog"],["dc.identifier.doi","10.4007/annals.2014.179.2.4"],["dc.identifier.gro","3146557"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4337"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Princeton University"],["dc.relation.issn","0003-486X"],["dc.subject","Cayley graphs graph diameters permutation groups"],["dc.title","On the diameter of permutation groups"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]