Sums of \(r\)-Lah numbers and \(r\)-Lah polynomials. (English) Zbl 1464.05013
Summary: The total number of partitions of a finite set into nonempty ordered subsets such that \(r\) distinguished elements belong to distinct ordered blocks can be described as sums of \(r\)-Lah numbers. In this paper we study this possible variant of Bell-like numbers, as well as the related \(r\)-Lah polynomials.
MSC:
| 05A18 | Partitions of sets |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 11B73 | Bell and Stirling numbers |
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