TY - JOUR
AU1 - Hejda, Tomáš
AB - Let 
$$\beta \in (1,2)$$



β
∈
(
1
,
2
)



 be a Pisot unit and consider the symmetric 
$$\beta $$


β


-expansions. We give a necessary and sufficient condition for the associated Rauzy fractals to form a tiling of the contractive hyperplane. For 
$$\beta $$


β


 a d-Bonacci number, i.e., Pisot root of 
$$x^d-x^{d-1}-\dots -x-1$$




x
d

-

x

d
-
1


-
⋯
-
x
-
1



 we show that the Rauzy fractals form a multiple tiling with covering degree 
$$d-1$$



d
-
1



.
TI - Multiple tilings associated to d-Bonacci beta-expansions
JF - Monatshefte für Mathematik
DO - 10.1007/s00605-018-1219-2
DA - 2018-08-14
UR - https://www.deepdyve.com/lp/springer-journals/multiple-tilings-associated-to-d-bonacci-beta-expansions-DOygZj30c0
SP - 275
EP - 291
VL - 187
IS - 2
DP - DeepDyve
ER -