All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 10 Next

Displaying 181 – 200 of 694

Showing per page

Periodicity of β-expansions for certain Pisot units*

Sandra Vaz, Pedro Martins Rodrigues (2012)

ESAIM: Proceedings

Given β > 1, let Tβ T β : [ 0 , 1 [ → [ 0 , 1 [ x → βx − ⌊ βx ⌋ . The 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 expansion x = ∑ i ≥ 0 e i β − i , where each ei...

Periodicity problem of substitutions over ternary alphabets

Bo Tan, Zhi-Ying Wen (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In this paper, we characterize the substitutions over a three-letter alphabet which generate a ultimately periodic sequence.

Periods of sets of lengths: a quantitative result and an associated inverse problem

Wolfgang A. Schmid (2008)

Colloquium Mathematicae

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...

Currently displaying 181 – 200 of 694