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View article: Shannon Weights for binary dynamical recurrent sources of zero entropy
Shannon Weights for binary dynamical recurrent sources of zero entropy Open
A probabilistic source is defined as the set of infinite words (over a given denumerable alphabet) endowed with a probability $μ$. The paper deals with general binary sources where the distribution of any symbol (0 or 1) may depend on an u…
View article: Poisson genericity in numeration systems with exponentially mixing probabilities
Poisson genericity in numeration systems with exponentially mixing probabilities Open
We define Poisson genericity for infinite sequences in any finite or countable alphabet with an invariant exponentially-mixing probability measure. A sequence is Poisson generic if the number of occurrences of blocks of symbols asymptotica…
View article: Lochs-type theorems beyond positive entropy
Lochs-type theorems beyond positive entropy Open
Lochs' theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a function of the number of digits given in some other expansion. In its original version, Loch…
View article: Two Arithmetical Sources and Their Associated Tries
Two Arithmetical Sources and Their Associated Tries Open
This article is devoted to the study of two arithmetical sources associated with classical partitions, that are both defined through the mediant of two fractions. The Stern-Brocot source is associated with the sequence of all the mediants,…
View article: Gaussian Behavior of Quadratic Irrationals
Gaussian Behavior of Quadratic Irrationals Open
We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with t…
View article: Irreducibility Criteria for Reciprocal Polynomials and Applications
Irreducibility Criteria for Reciprocal Polynomials and Applications Open
We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a consequence of our app…