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Two notes on notation. (English) Zbl 0785.05014
This is an enthusiastic and well-written case for two changes of notation. The first concerns the Iverson convention: if $$P$$ is a statement, $$[P]$$ is defined to be 1 if $$P$$ is true and 0 if $$P$$ is false. Thus for example $\sum_{k\text{ odd}} f(k)= \sum_ k f(k)[k\text{ odd}].$ The second concerns Stirling numbers, where at present there is no universally accepted standard notation. Knuth’s proposal is based on a suggestion of I. Marx [ibid. 69, 530-532 (1962; Zbl 0136.356)] and is to use $${n\brack k}$$ to denote the number of permutations of $$n$$ objects having $$k$$ cycles, and $${n\brace k}$$ to denote the number of partitions of $$n$$ objects into $$k$$ nonempty subsets. Much fascinating historical information is included as the case for these proposals is presented.

##### MSC:
 05A99 Enumerative combinatorics
##### Keywords:
notation; Stirling numbers
Zbl 0136.356
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