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
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.
Full version: pdf,
(Concerned with sequences
Received April 29 2015; revised version received August 25 2015.
Published in Journal of Integer Sequences,
September 8 2015.
Journal of Integer Sequences home page