Generator-offset property: Difference between revisions
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Case 1: Λ<sub>2</sub> is the mos (n − 2)β 2β’. | Case 1: Λ<sub>2</sub> is the mos (n − 2)β 2β’. | ||
For Λ<sub>2</sub> to be a mos, the first occurrence of R must be at either f = floor(n/2) or ceil(n/2). We may assume that it is at f; otherwise flip the chain and reindex the words to start at 2f. | For Λ<sub>2</sub> to be a mos, the first, and only, occurrence of R must be at either f = floor(n/2) or ceil(n/2). We may assume that it is at f; otherwise flip the chain and reindex the words to start at 2f. | ||
1 … f … 2f n | 1 … f … 2f n | ||
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We need only consider stacks up to f-many k-steps. Either: | We need only consider stacks up to f-many k-steps. Either: | ||
# the stack has only preimages of P’s and it either contains | # the stack has only preimages of P’s and it either contains R or not; or | ||
# the stack has one T and does not contain any R (since it’s more than f − 1 generators away). | # the stack has one T and does not contain any R (since it’s more than f − 1 generators away). | ||
These give exactly three distinct sizes for every interval class. Hence S is SV3. | These give exactly three distinct sizes for every interval class. Hence S is SV3. | ||