Permutations with Ascending and Descending Blocks
arXiv:0908.4347
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.
17 pages, 6 figures, glossary; v2: added reference to earlier version of Corollary 3.1 in [3]