Geodesic
Enumeration of two particular sets of minimal permutations
Journal of integer sequences, Tome 18 (2015) no. 10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Bilotta, Stefano and Grazzini, Elisabetta and Pergola, Elisa},
     title = {Enumeration of two particular sets of minimal permutations},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2015},
     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/