Publications of (and about) Paul Erdös
Autor: Erdös, Paul; Guy, Richard K.; Moon, J.W.
Title: On refining partitions. (In English)
Source: J. London Math. Soc., II. Ser. 9, 565-570 (1975).
Review: A partition of a set is refined by splitting one of the subsets into two smaller subsets. Let f(n) denote the number of ways of transforming n indistinguishable objects into n singletons via a sequence of n-1 refinements. The authors show that there exist constants c1 and c2 such that cn1nn/2 < f(n) < cn2nn/2. They also show that the nummer of ways of transforming a set of n distinguishable objects into n singletons is n!(n-1)/2n-1.
Classif.: * 05A17 Partitions of integres (combinatorics)
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