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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, $\left[P\right]$ is defined to be 1 if $P$ is true and 0 if $P$ is false. Thus for example

$\sum _{k\phantom{\rule{4.pt}{0ex}}\text{odd}}f\left(k\right)=\sum _{k}f\left(k\right)\left[k\phantom{\rule{4.pt}{0ex}}\text{odd}\right]·$

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 $\left[\genfrac{}{}{0pt}{}{n}{k}\right]$ to denote the number of permutations of $n$ objects having $k$ cycles, and $\left\{\genfrac{}{}{0pt}{}{n}{k}\right\}$ 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 Classical combinatorial problems
Keywords:
notation; Stirling numbers