Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 7.4.2015 |
| Speaker: | Tomáš Hejda, FJFI, České vysoké učení technické v Praze |
| Title: | Multiple tilings associated to the symmetric $d$-Bonacci expansions |
| Abstract: | It is a well-known fact that when $\beta$ is a $d$-Bonacci number, the Rauzy fractals arising from the greedy (Rényi) beta-transformation tile the contracting hyperplane. However, it was recently shown that the Rauzy fractals arising in the symmetric Tribonacci transformation form a double tiling, i.e., almost every point of the hyperplane lies in exactly 2 tiles. We show that the covering degree for the symmetric $d$-Bonacci transformation is equal to $d-1$. We moreover characterize which tiles lie in the same layer of the multiple tiling. We finish by several related open questions. |
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