2009/08/23 by Jacob Steinhardt, Steinhardt, Jacob
Computer Science · Mathematics · #05A05 #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A19
paper · pdf · doi:10.48550/arxiv.0908.3330
15 pages, 3 figures, updated information for reference [9] in v2
openalex publication_date 2009/08/23 · arxiv created 2009/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the work of Eriksen, Freij, and Wastlund [3], who study derangements that descend in blocks of prescribed lengths. We generalize their work to derangements that ascend in some blocks and descend in others. In particular, we obtain a generating function for the derangements that ascend in blocks of prescribed lengths, thus solving a problem posed in [3]. We also work towards a combinatorial interpretation of a polynomial sum appearing in [3]. As a result, we obtain a new combinatorial sum for counting derangements with ascending and descending blocks.