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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.

05A99 Enumerative combinatorics
Zbl 0136.356
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