Generator-offset property: Difference between revisions

@@ Line 198: / Line 198: @@
 Λ<sub>2</sub> has two consecutive chunks of size 1. Since chunk sizes of a mos themselves form a mos, Λ<sub>2</sub> 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, 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'' &minus; 1) : (''n'' &minus; 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'' &minus; 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:
+Λ<sub>2</sub> has only two chunks of size 1, Λ<sub>2</sub>[(''n'' &minus; 1) : (''n'' &minus; 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'' &minus; 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:
 2  3 4 5  6 7