Let S be an alphabet with k letters . If there are arbitrarily long words over S avoiding p , we say that p is avoidable on S . Crown Let n be an even number. Let w be an omega-word . The essence of w , denoted by Ess w is the set of all finite subwords of w that appear in w as subwords infinitely often.
Fence Let n be an even number.
Thus a repetition is a 2-power. Occurrence Let y be a subword of w . One specific place where y shows up in w is called an occurrence of y in w . We call a countably infinite sequence of letters of S an omega-word over S . S is perfect if it is non-empty, closed and contains no isolated points.