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Range of density measures

Martin Sleziak, Miloš Ziman (2009)

Acta Mathematica Universitatis Ostraviensis

We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence A ( n ) n as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...

Reading along arithmetic progressions

T. Downarowicz (1999)

Colloquium Mathematicae

Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.

Récurrences 2 - et 3 -mahlériennes

Bernard Randé (1993)

Journal de théorie des nombres de Bordeaux

On sait (Cobham) qu’une suite 2 - et 3 -automatique est une suite rationnelle. Une question de Loxton et van der Poorten étend ce résultat au cas 2 - et 3 -régulier. On montre dans cet article que, si une suite vérifie une récurrence 2 - et 3 -mahlérienne d’ordre un, elle est rationnelle.

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