Derangements with Ascending and Descending Blocks

Details Derangements with Ascending and Descending Blocks Derangements with Ascending and Descending Blocks

2009-08-23

arxiv.org/abs/0908.3330v2

Mathematics

Combinatorics

15 pages, 3 figures, updated information for reference [9] in v2

Scientific paper

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.

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