Permutations with Ascending and Descending Blocks
Combinatorics
2009-09-01 v2
Abstract
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then provide the first bijective proofs of some known results. We also solve some problems posed in [3] by Eriksen, Freij, and Wastlund, who study derangements that descend in blocks of prescribed lengths.
Cite
@article{arxiv.0908.4347,
title = {Permutations with Ascending and Descending Blocks},
author = {Jacob Steinhardt},
journal= {arXiv preprint arXiv:0908.4347},
year = {2009}
}
Comments
17 pages, 6 figures, glossary; v2: added reference to earlier version of Corollary 3.1 in [3]