Multi-statistic enumeration of two-stack sortable permutations

Using Zeilberger’s factorization of two-stack-sortable permutations, we write a functional equation — of a strange sort — that defines their generating function according to five statistics: length, number of descents, number of right-to-left and left-to-right maxima, and a fifth statistic that is closely linked to the factorization. Then, we show how one can translate this functional equation into a polynomial one. We thus prove that our five-variable generating function for two-stack-sortable permutations is algebraic of degree 20.

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: Mireille Bousquet-Mélou
• Keywords: COMBINATORICS 1998, Functional Equation, Generating Function, Two-stack-sortable Permutations