March 7, 2002 PERMUTATION PATTERNS, ORDERED TREES AND CONTINUED FRACTIONS
نویسنده
چکیده
We enumerate permutations which have exactly r 123-patterns and s 132patterns where r + s ≤ 2. We also give a new bijection between the ordered trees on n+1 vertices and 123-avoiding permutations of length n. We define the weight of ordered trees so that the bijection becomes weight-preserving, and find the generating function, in the form of a continued fraction, of 123-avoiding permutations of length n that have exactly r 132-patterns.
منابع مشابه
Continued Fractions and Catalan Problems
We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of (132)-pattern avoiding permutations that have a given number of increasing patt...
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