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dc.contributor.authorAlbert, M.D.
dc.contributor.authorRuskuc, Nik
dc.contributor.authorVatter, V.
dc.identifier.citationAlbert , M D , Ruskuc , N & Vatter , V 2015 , ' Inflations of geometric grid classes of permutations ' , Israel Journal of Mathematics , vol. 205 , no. 1 , pp. 73-108 .
dc.identifier.otherPURE: 106032568
dc.identifier.otherPURE UUID: 7dc77a68-8ff0-41bf-a631-626e7253c768
dc.identifier.otherScopus: 84928658406
dc.identifier.otherWOS: 000350877400003
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702047
dc.descriptionAll three authors were partially supported by EPSRC via the grant EP/J006440/1.en
dc.description.abstractGeometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of permutation classes of growth rate less than κ ≈ 2.20557 (a specific algebraic integer at which infinite antichains first appear). Using language- and order-theoretic methods, we prove that the substitution closures of geometric grid classes are well partially ordered, finitely based, and that all their subclasses have algebraic generating functions. We go on to show that the inflation of a geometric grid class by a strongly rational class is well partially ordered, and that all its subclasses have rational generating functions. This latter fact allows us to conclude that every permutation class with growth rate less than κ has a rational generating function. This bound is tight as there are permutation classes with growth rate κ which have nonrational generating functions.
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.rights© 2014. The Hebrew University Magnes Press. This is the accepted version of the following article: This is the preprint version before acceptance of the following article: Exact dimensionality and projections of random self-similar measures and sets Falconer, K. & Jin, X. 2014 In : Journal of the London Mathematical Society. The final publication is available at Springer via
dc.subjectQA Mathematicsen
dc.titleInflations of geometric grid classes of permutationsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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