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.
Enumeration of Two Particular Sets of Minimal Permutations / Bilotta, Stefano; Grazzini, Elisabetta; Pergola, Elisa. - In: JOURNAL OF INTEGER SEQUENCES. - ISSN 1530-7638. - ELETTRONICO. - 18, Article 15.10.2:(2015), pp. 1-14.
Enumeration of Two Particular Sets of Minimal Permutations
BILOTTA, STEFANO;GRAZZINI, ELISABETTA;PERGOLA, ELISA
2015
Abstract
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.File | Dimensione | Formato | |
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