arXiv:0906.2795 [math.CO]AbstractReferencesReviewsResources
Descent sets of cyclic permutations
Published 2009-06-15, updated 2012-01-31Version 2
We present a bijection between cyclic permutations of {1,2,...,n+1} and permutations of {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. This non-trivial bijection involves a Foata-like transformation on the cyclic notation of the permutation, followed by certain conjugations. We also give an alternate derivation of the consequent result about the equidistribution of descent sets using work of Gessel and Reutenauer. Finally, we prove a conjecture of the author in [SIAM J. Discrete Math. 23 (2009), 765-786] and a conjecture of Eriksen, Freij and W\"astlund.
Comments: 22 pages, final journal version
Journal: Adv. in Appl. Math. 47 (2011), 688-709
Categories: math.CO
Tags: journal article
Related articles: Most relevant | Search more
arXiv:1710.05103 [math.CO] (Published 2017-10-13)
Exact and asymptotic enumeration of cyclic permutations according to descent set
arXiv:1008.1514 [math.CO] (Published 2010-08-09)
Moments of an exponential functional of random walks and permutations with given descent sets
Descent sets on 321-avoiding involutions and hook decompositions of partitions