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This book is devoted to the study of beta-integers, an equivalent of integers in the so-called Rényi nonstandard numeration systems where instead of an integer base, one considers irrational bases. This book includes results concerning arithmetics of beta-integers, combinatorics on words coding distances between consecutive beta-integers, and applications in the theory of quasicrystals.

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Since 2008 the author has been working as a teacher and researcher at the Czech Technical University in Prague. Her main research interests include Combinatorics on Words, Nonstandard Numeration Systems, Applications in Cryptology. She is the laureate of the UNESCO-L´Oréal award For Women in Science in the Czech Republic (2013).

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