Journal Article10.1017/ETDS.2014.69
Combinatorial and probabilistic properties of systems of numeration
Guy Barat,Peter J. Grabner +1 more
TL;DR: In this article, the authors studied the system of numeration defined by a strictly increasing sequence of positive integers by looking at the corresponding compactification K-G of N and the extension of the addition-by-one map tau on k-G (the "odometer").
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Abstract: 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 tau on K-G (the 'odometer'). We give sufficient conditions for the existence and uniqueness of tau-invariant measures on K-G in terms of combinatorial properties of G.
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Citations
The carry propagation of the successor function
TL;DR: In this article, the authors considered the problem of the amortized carry propagation in non-standard numeration systems of various kinds: abstract numeration, rational base numeration system, greedy numeration and beta-numeration.
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Problems from various branches of mathematics
I. M. I︠A︡glom,A. M. I︠A︡glom +1 more
- 01 Jan 1987
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The level of distribution of the sum-of-digits function of linear recurrence number systems
TL;DR: In this article , the authors studied the sum-of-digits function s G (ν)=ε 0 (ν)+⋯+ε ℓ (ν) under certain natural assumptions on the sequence G. In particular, they determined its level of distribution x ϑ .
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The level of distribution of the sum-of-digits function of linear recurrence number systems
TL;DR: In this paper, it was shown that for a strictly increasing linear recurrent sequence of integers with characteristic polynomial coefficients, the greedy expansion of a positive integer can be expressed by the so-called greedy expansion.
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References
•Book
Algebraic Combinatorics on Words
M. Lothaire
- 01 Jan 2002
TL;DR: In this article, Berstel and Perrin proposed the concept of Sturmian words and the plactic monoid, which is a set of permutations and infinite words.
2K
•Book
Topological Vector Spaces II
h.c. Gottfried Köthe
- 19 Dec 1979
TL;DR: In this article, the elementary theory of normed spaces and Banach spaces is discussed, and a number of classical examples are discussed, to which we shall refer time and again in the later parts of the book.
1.5K
Nombres algébriques et substitutions
TL;DR: In this paper, the conditions générales d'utilisation of commercial or impression systématique for copyright violation are discussed. But they do not consider the effect of the impression of a fichier on copyright.