Geodesic
Multi-static enumeration of two-stack sortable permutations
The electronic journal of combinatorics, Tome 5 (1998)
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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.
DOI : 10.37236/1359
Classification : 05A15, 05A05, 05C30, 68R10
Mots-clés : enumeration, two-stack-sortable permutations, statistics, generating function 
@article{10_37236_1359,
     author = {Mireille Bousquet-M\'elou},
     title = {Multi-static enumeration of two-stack sortable permutations},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1359},
     zbl = {0890.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1359/}
}
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Mireille Bousquet-Mélou. Multi-static enumeration of two-stack sortable permutations. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1359

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