Bell numbers and \(k\)-trees. (English) Zbl 0857.05010
The author shows that the number of partitions of \(\{1,2,\dots,n\}\) such that if \(0<|i-j|\leq a\) then \(i\) and \(j\) belong to different blocks is the Bell number \(B_{n-a}\).
Reviewer: J.W.Moon (Edmonton)
MSC:
05A17 | Combinatorial aspects of partitions of integers |
05C05 | Trees |
11B73 | Bell and Stirling numbers |
Online Encyclopedia of Integer Sequences:
Bell or exponential numbers: number of ways to partition a set of n labeled elements.References:
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