2009/08/23 by Steinhardt, Jacob
#05A05 #05A19 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0908.3330
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.