Generalized Schr?der permutations

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• 作者：Elena Barcucci ; Vincent Vajnovszki
• 关键词：Pattern avoiding permutations ; Generating function ; Generating trees ; Schrö ; der ; Catalan and central binomial coefficient number
• 刊名：Theoretical Computer Science
• 出版年：2013
• 出版时间：2 September, 2013
• 年：2013
• 卷：502
• 期：Complete
• 页码：210-216
• 全文大小：306 K

文摘

We give the generating function for the integer sequence enumerating a class of pattern avoiding permutations depending on two parameters: and . The avoided patterns are the permutations of length with the largest element in the first position and the second largest in one of the last positions. For particular instances of and we obtain pattern avoiding classes enumerated by Schr?der, Catalan and central binomial coefficient numbers, and thus, the obtained two-parameter generating function gathers under one roof known generating functions and expresses new ones. This work generalizes some earlier results of Barcucci et?al. (2000)? , Kremer (2000)? and Kremer (2003)? .