Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 14.4.2015 |
| Speaker: | Tomáš Hejda, FJFI, České vysoké učení technické v Praze |
| Title: | Multiple tilings associated to the symmetric $d$-Bonacci expansions II. Proofs |
| Abstract: | It is a well-known fact that when $\beta$ is a $d$-Bonacci number, the Rauzy fractals arising from the greedy (R\'enyi) 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. In this second talk, we give the proofs of the statements. We finish by several related open questions. |
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