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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
Citations:
Zbl 0136.356
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