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Unformatted text preview: 8/27
we ﬁnd x1 = 4/13. Similar calculations give x2 = 10/13 and x3 = 12/13.
Applying Prop. 2.4.1, we see these points x1 , x2 , and x3 constitute a 3-cycle in
the sense that T2 (x1 ) = x2 , T2 (x2 ) = x3 , and T1 (x3 ) = x1 .
PrxsSol 2.4.2 These forbidden compositions mean the length 2 addresses 11,
21, 31, and 41 are empty. Following the reasoning of Example 2.4.2, we see
that every address containing 11, 21, 31, or 41 must be empty. These addresses
are of two kinds, illustrated by length 3 addresses. For example, addresses
of the form 11i belong to subsquares of 11, necessarily empty because 11 is
empty. In general, address digits appended to the right of a forbidden address
ij · · · k refer to subregions of the forbidden address ij · · · k , and so needn’t be
listed separately. On the other hand, appending address digits to the left of a
forbidden address ij · · · k often gives addresses of regions that are not subregions
of ij · · · k , and these should be listed separately. See Fig. 2.30. The forbidden
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