Intervals of permutation class growth rates

Research output: Contribution to journalArticle

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θB ≈ 2.35526, and that it also contains every value at least λB ≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λA ≈ 2.48187. Thus, we also refute his conjecture that the set of growth rates below λA is nowhere dense. Our proof is based upon an analysis of expansions of real numbers in non-integer bases, the study of which was initiated by Rényi in the 1950s. In particular, we prove two generalisations of a result of Pedicini concerning expansions in which the digits are drawn from sets of allowed values.
Original languageEnglish
Number of pages26
JournalCombinatorica
StateAccepted/In press - 4 Apr 2016

    Research areas

  • permutation classes, growth rates, expansions in noninteger bases

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