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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.00578 |
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| _version_ | 1866916344799166464 |
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| author | Calegari, Danny |
| author_facet | Calegari, Danny |
| contents | The Tautological Lamination arises in holomorphic dynamics as a combinatorial model for the geometry of 1-dimensional slices of the Shift Locus. In each degree $q$ the tautological lamination defines an iterated sequence of partitions of $1$ (one for each integer $n$) into numbers of the form $2^m q^{-n}$. Denote by $N_q(n,m)$ the number of times $2^mq^{-n}$ arises in the $n$th partition. We prove a recursion formula for $N_q(n,0)$, and a gap theorem: $N_q(n,n)=1$ and $N_q(n,m)=0$ for $\lfloor n/2 \rfloor < m < n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_00578 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Combinatorics of the Tautological Lamination Calegari, Danny Dynamical Systems Combinatorics 37F10, 68R15 The Tautological Lamination arises in holomorphic dynamics as a combinatorial model for the geometry of 1-dimensional slices of the Shift Locus. In each degree $q$ the tautological lamination defines an iterated sequence of partitions of $1$ (one for each integer $n$) into numbers of the form $2^m q^{-n}$. Denote by $N_q(n,m)$ the number of times $2^mq^{-n}$ arises in the $n$th partition. We prove a recursion formula for $N_q(n,0)$, and a gap theorem: $N_q(n,n)=1$ and $N_q(n,m)=0$ for $\lfloor n/2 \rfloor < m < n$. |
| title | Combinatorics of the Tautological Lamination |
| topic | Dynamical Systems Combinatorics 37F10, 68R15 |
| url | https://arxiv.org/abs/2106.00578 |