Permutations with Ascending and Descending Blocks

Details Permutations with Ascending and Descending Blocks Permutations with Ascending and Descending Blocks

2009-08-29

arxiv.org/abs/0908.4347v2

Mathematics

Combinatorics

17 pages, 6 figures, glossary; v2: added reference to earlier version of Corollary 3.1 in [3]

Scientific paper

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.

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