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math.NT2025
Unique expansions in number systems via refinement equations
Sergei V. Konyagin, Vladimir Yu. Protasov, Alexey L. Talambutsa
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the -ary number system with a set of non-negative i…
math.RA2025
Perron matrix semigroups
Vladimir Yu. Protasov
We consider multiplicative semigroups of real dxd matrices. A semigroup S is called Perron if each of its matrices has a Perron eigenvalue, i.e., an eigenvalue equal to the spectra…