Rank-3 scale theorems: Difference between revisions
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
* Every max variety 3 block is a triple Fokker block. (However, not every max-variety 3 scale, in general, need be a Fokker block.) | * Every max variety 3 block is a triple Fokker block. (However, not every max-variety 3 scale, in general, need be a Fokker block.) | ||
* Triple Fokker blocks form a [http://en.wikipedia.org/wiki/Trihexagonal_tiling trihexagonal tiling] on the lattice. | * Triple Fokker blocks form a [http://en.wikipedia.org/wiki/Trihexagonal_tiling trihexagonal tiling] on the lattice. | ||
* A scale imprint is that of a Fokker block if and only if it is the [[product word]] of two DE scale imprints with the same number of notes. See [https://link.springer.com/chapter/10.1007/978-3-642-21590-2_24 Introduction to Scale Theory over Words in Two Dimensions | SpringerLink] | * A scale imprint is that of a Fokker block if and only if it is the [[product word|product]] of two DE scale imprints with the same number of notes. See [https://link.springer.com/chapter/10.1007/978-3-642-21590-2_24 Introduction to Scale Theory over Words in Two Dimensions | SpringerLink] | ||
* If the step sizes for a rank-3 Fokker block are L, m, n, and s, where L > m > n > s, then the following identity must hold: (n-s) + (m-s) = (L-s), hence n+m=L+s | * If the step sizes for a rank-3 Fokker block are L, m, n, and s, where L > m > n > s, then the following identity must hold: (n-s) + (m-s) = (L-s), hence n+m=L+s | ||
* Any convex object on the lattice can be converted into a hexagon. | * Any convex object on the lattice can be converted into a hexagon. | ||