Combinatorial and probabilistic properties of systems of numeration

Peter J. Grabner
Technische Universität Graz

Date(s) : 14/04/2015   iCal
11 h 40 min - 12 h 20 min

Let G=(G_n)_n be a strictly increasing sequence of positive integers with G_0=1. We study the system of numeration defined by this sequence by looking at the corresponding compactification K_G of ℕ and the extension of the addition-by-one map τ on K_G (the “odometer”). We give sufficient conditions for the existence and uniqueness of τ-invariant measures on K_G in terms of combinatorial properties of G.



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