Geodesic
Equivalences for pattern avoiding involutions and classification
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of $S_5$, $S_6$, and $S_7$ for both permutations and involutions. 
@article{DMTCS_2008_special_255_a45,
     author = {Dukes, Mark and Jel{\'\i}nek, V{\'\i}t and Mansour, Toufik and Reifegerste, Astrid},
     title = {Equivalences for pattern avoiding involutions and classification},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3637},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3637/}
}
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Dukes, Mark; Jelínek, Vít; Mansour, Toufik; Reifegerste, Astrid. Equivalences for pattern avoiding involutions and classification. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3637. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3637/

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