Ternary scale theorems: Difference between revisions
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(b) The following proof is taken from "Balanced Sequences and Optimal Routing", by Altman, Gaujal, and Hordijk (2000). | (b) The following proof is taken from "Balanced Sequences and Optimal Routing", by Altman, Gaujal, and Hordijk (2000). | ||
Let ''W'' be the (balanced) right-infinite word made by concatenating infinitely many copies of ''s''. We use the following steps: | Let ''W'' be the (balanced) right-infinite word made by concatenating infinitely many copies of ''s''. We use the following steps, using the balance property: | ||
(i) The sequence '''XZX''' must appear in ''W''. | (i) The sequence '''XZX''' must appear in ''W''. | ||