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math.NT2026
Non-Expansive Matrix Based number Systems
Adam Blažek, Kevin G. Hare, Edita Pelantová
An integer -dimensional vector is usually represented by strings, which express the value of each component separately. This article is devoted to number systems that allow…
math.NT2026
Matrices with cyclically monotone rows and Cantor numeration systems
Pavel Šťovíček, Edita Pelantová
We study a class of square matrices with non-negative elements which have cyclically monotone rows in the sense that each row of a matrix from the class consists of a cyclically no…
math.NT2026
Parry condition, existence and uniqueness of alternate bases
Émilie Charlier, Savinien Kreczman, Zuzana Masáková +1
Alternate bases are a numeration system that generalizes the Rényi numeration system. It is common in this context to construct examples or counter-examples by specifying the expan…