Geodesic
Enumeration of permutations sorted with two passes through a stack and D_8 symmetries
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We examine the sets of permutations that are sorted by two passes through a stack with a $D_8$ operation performed in between. From a characterization of these in terms of generalized excluded patterns, we prove two conjectures on their enumeration, that can be refined with the distribution of some statistics. The results are obtained by generating trees. 
@article{DMTCS_2012_special_263_a66,
     author = {Bouvel, Mathilde and Guibert, Olivier},
     title = {Enumeration of permutations sorted with two passes through a stack and {D_8} symmetries},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3080},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3080/}
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Bouvel, Mathilde; Guibert, Olivier. Enumeration of permutations sorted with two passes through a stack and D_8 symmetries. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3080. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3080/

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