Generator-offset property: Difference between revisions
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Λ<sub>2</sub> has two consecutive chunks of size 1. Since chunk sizes form a mos, Λ<sub>2</sub> has more chunks of size 1 than it has chunks of size 2. | Λ<sub>2</sub> has two consecutive chunks of size 1. Since chunk sizes form a mos, Λ<sub>2</sub> has more chunks of size 1 than it has chunks of size 2. | ||
Use | Use w[i : j] to denote the slice of the cyclic word w that includes both endpoints, i.e. the word w[i] w[i + 1] ... w[j] where indices are taken to be elements of '''Z'''/n'''Z'''. Λ<sub>2</sub> has only two chunks of size 1, Λ<sub>2</sub>[(n − 1) : (n − 1)] and Λ<sub>2</sub>[1 : 1], since otherwise Λ<sub>3</sub> would have a chunk of size 1 within Λ<sub>3</sub>[1 : (n − 1)]. Thus Λ<sub>2</sub> has exactly one chunk of size 2. Thus Λ<sub>2</sub> = ββ’βββ’ββ’ and Λ<sub>3</sub> = γγ’γγγ’γγ. Thus we have: | ||
1 2 3 4 5 6 7 | 1 2 3 4 5 6 7 | ||