Geodesic
Enumeration of two particular sets of minimal permutations
Journal of integer sequences, Tome 18 (2015) no. 10
Minimal permutations with $d$ descents and size $d + 2$ have a unique ascent between two sequences of descents. Our aim is the enumeration of two particular sets of these permutations. The first set contains the permutations having $d + 2$ as the top element of the ascent. The permutations in the latter set have 1 as the last element of the first sequence of descents and are the reverse-complement of those in the other set. The main result is that these sets are enumerated by the second-order Eulerian numbers.
Classification : 05A15, 05A05
Keywords: minimal permutation, enumeration 
@article{JIS_2015__18_10_a7,
     author = {Bilotta,  Stefano and Grazzini,  Elisabetta and Pergola,  Elisa},
     title = {Enumeration of two particular sets of minimal permutations},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1328.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a7/}
}
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Bilotta,  Stefano; Grazzini,  Elisabetta; Pergola,  Elisa. Enumeration of two particular sets of minimal permutations. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a7/