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Displaying 181 –
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694
Given β > 1, let TβThe iteration of this transformation gives rise to the greedy β-expansion.
There has been extensive research on the properties of this expansion and its dependence
on the parameter β.In [17], K. Schmidt analyzed the set of periodic points of
Tβ, where β is a Pisot
number. In an attempt to generalize some of his results, we study, for certain Pisot
units, a different expansion that we call linear expansionwhere each ei...
In this paper, we characterize the substitutions over a three-letter alphabet which generate a ultimately periodic sequence.
In this paper, we characterize the substitutions over a
three-letter alphabet which generate a ultimately periodic
sequence.
The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...
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