Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.2

Enumeration of Two Particular Sets of Minimal Permutations

Stefano Bilotta, Elisabetta Grazzini, and Elisa Pergola
Dipartimento di Matematica e Informatica "Ulisse Dini"
Università di Firenze
Viale G. B. Morgagni 65
50134 Firenze


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.

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(Concerned with sequences A000918 A005803.)

Received April 29 2015; revised version received August 25 2015. Published in Journal of Integer Sequences, September 8 2015.

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