Abstract
We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.
| Original language | American English |
|---|---|
| Pages (from-to) | 81-91 |
| Number of pages | 11 |
| Journal | Notes on Number Theory and Discrete Mathematics |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2022 |
Keywords
- Generating function
- Isolated succession
- Partition
- Recurrence