Run Distribution Over Flattened Partitions
Title | Run Distribution Over Flattened Partitions |
Publication Type | Journal Article |
Year of Publication | 2020 |
Authors | Nabawanda, O, Rakotondrajao, F, Bamunoba, ASamuel |
Journal | Integer Seq |
Volume | 23 |
Issue | 9 |
Pagination | 14 |
Abstract | The study of flattened partitions is an active area of current research. In this paper, our study unexpectedly leads us to the OEIS sequence A124324. We provide a new combinatorial interpretation of these numbers. A combinatorial bijection between flattened partitions over [n + 1] and the partitions of [n] is also given in a separate section. We introduce the numbers fn,k, which count the number of flattened partitions over [n] having k runs. We give recurrence relations defining them, as well as their exponential generating function in differential form. It should be appreciated if its closed form is established. We extend the results to flattened partitions where the first s integers belong to different runs. Combinatorial proofs are given. |
URL | https://cs.uwaterloo.ca/journals/JIS/VOL23/Nabawanda/naba5.html |