Geodesic
Enumerating permutations avoiding more than three Babson-Steingrímsson patterns
Journal of integer sequences, Tome 10 (2007) no. 6
Claesson and Mansour recently proposed some conjectures about the enumeration of the permutations avoiding more than three Babson-Steingrímsson patterns (generalized patterns of type (1,2) or (2,1)). The avoidance of one, two or three patterns has already been considered. Here, the cases of four and five forbidden patterns are solved and the exact enumeration of the permutations avoiding them is given, confirming the conjectures of Claesson and Mansour. The approach we use can be easily extended to the cases of more than five forbidden patterns.
Classification : 05A15, 05A05
Keywords: generalized pattern avoidance, babson-steingrímsson patterns, permutations 
@article{JIS_2007__10_6_a6,
     author = {Bernini,  Antonio and Pergola,  Elisa},
     title = {Enumerating permutations avoiding more than three {Babson-Steingr{\'\i}msson} patterns},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {6},
     zbl = {1144.05002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_6_a6/}
}
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Bernini,  Antonio; Pergola,  Elisa. Enumerating permutations avoiding more than three Babson-Steingrímsson patterns. Journal of integer sequences, Tome 10 (2007) no. 6. http://geodesic.mathdoc.fr/item/JIS_2007__10_6_a6/