Generator-offset property: Difference between revisions
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Λ2 has two consecutive chunks of size 1. Since chunk sizes form a mos, Λ2 has more chunks of size 1 than it has chunks of size 2. | Λ2 has two consecutive chunks of size 1. Since chunk sizes form a mos, Λ2 has more chunks of size 1 than it has chunks of size 2. | ||
Use “w[i:j]” to denote the slice of the cyclic word w that includes both endpoints. Λ2 has only two chunks of size 1, Λ2[(n − 1):(n − 1)] and Λ2[1:1], since otherwise Λ3 would have a chunk of size 1 within Λ3[1:n − 1]. Thus Λ2 has exactly one chunk of size 2. Thus Λ2 = ββ’βββ’ββ’ and Λ3 = γγ’γγγ’γγ. Thus we have: | 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'''. Λ2 has only two chunks of size 1, Λ2[(n − 1):(n − 1)] and Λ2[1:1], since otherwise Λ3 would have a chunk of size 1 within Λ3[1:n − 1]. Thus Λ2 has exactly one chunk of size 2. Thus Λ2 = ββ’βββ’ββ’ and Λ3 = γγ’γγγ’γγ. Thus we have: | ||
1 2 3 4 5 6 7 | 1 2 3 4 5 6 7 | ||