The Number of Permutations Realized By a Shift
نویسنده
چکیده
A permutation π is realized by the shift on N symbols if there is an infinite word on an N -letter alphabet whose successive left shifts by one position are lexicographically in the same relative order as π. The set of realized permutations is closed under consecutive pattern containment. Permutations that cannot be realized are called forbidden patterns. It was shown in [1] that the shortest forbidden patterns of the shift on N symbols have length N + 2. In this paper we give a characterization of the set of permutations that are realized by the shift on N symbols, and we enumerate them according to their length.
منابع مشابه
Permutations realized by shifts
A permutation π is realized by the shift on N symbols if there is an infinite word on an N -letter alphabet whose successive left shifts by one position are lexicographically in the same relative order as π. The set of realized permutations is closed under consecutive pattern containment. Permutations that cannot be realized are called forbidden patterns. It was shown in [J.M. Amigó, S. Elizald...
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 23 شماره
صفحات -
تاریخ انتشار 2009