# Intervals of permutation class growth rates

Research output: Contribution to journal › Article

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θ

_{B}≈ 2.35526, and that it also contains every value at least λ_{B}≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λ_{A}≈ 2.48187. Thus, we also refute his conjecture that the set of growth rates below λ_{A}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 language | English |
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Number of pages | 26 |

Journal | Combinatorica |

State | Accepted/In press - 4 Apr 2016 |

- permutation classes, growth rates, expansions in noninteger bases

### Research areas

## Publications

(1)## On the growth of permutation classes

Research output: Thesis › Doctoral Thesis