Inversion polynomials for 321-avoiding permutations

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• 作者：Szu-En Cheng ; Sergi Elizalde ; Anisse Kasraoui ; Bruce E. Sagan
• 关键词：Catalan number ; Continued fraction ; Dyck path ; Generating function ; Pattern avoidance ; Permutation ; Inversion number ; Major index ; Motzkin path ; Polyomino ; qq-analogue
• 刊名：Discrete Mathematics
• 出版年：2013
• 出版时间：28 November, 2013
• 年：2013
• 卷：313
• 期：22
• 页码：2552-2565
• 全文大小：443 K

文摘

We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formula for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin paths, polyominoes, and continued fractions.