Permutations with Ascending and Descending Blocks

2009/08/29 by Jacob Steinhardt, Steinhardt, Jacob
Computer Science · Engineering · Mathematics · #05A05 #05A19 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0908.4347

openalex publication_date 2009/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Alternating permutations and symmetric functions

Related

• Derangements with Ascending and Descending Blocks
• The cycle descent statistic on permutations
• The excedances and descents of bi-increasing permutations
• On Connection between the Numbers of Permutations and Full Cycles with\n Some Restrictions on Positions and Up-Down Structure
• A simple bijection between permutation matrices and descending plane partitions without special parts