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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 $$\sum\sb{k\text{ odd}} f(k)= \sum\sb k f(k)[k\text{ odd}].$$ The second concerns Stirling numbers, where at present there is no universally accepted standard notation. Knuth’s proposal is based on a suggestion of {\it 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.

05A99Classical combinatorial problems
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