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:
| [1] | Beineke, L. W.; Pippert, R. E., The number of labeled \(k\)-dimensional trees, J. Combin. Theory, 6, 200-205 (1969) · Zbl 0175.20904 |
| [2] | (Erdős, P.; Renyi, A.; Sós, A. T., Combinatorial Theory and its Applications III (1970), Bolyai János Matematikai Társulat: Bolyai János Matematikai Társulat Budapest, Hungary), 945-946 |
| [3] | Moon, J. W., The number of labeled \(k\)-trees, J. Combin. Theory, 6, 196-199 (1969) · Zbl 0175.50203 |
| [4] | Read, R. C., Contributions to the cell growth problem, Canad. J. Math., 14, 1-20 (1962) · Zbl 0105.13510 |
| [5] | van Lint, J. H.; Wilson, R. M., A Course in Combinatorics, ((1992), Cambridge University Press: Cambridge University Press Cambridge), 105 · Zbl 0769.05001 |
| [6] | Whitehead, E. G., Enumerative Combinatorics, ((1972), Courant Institute of Mathematical Sciences: Courant Institute of Mathematical Sciences New York University), 8-13 · Zbl 0283.05007 |
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