Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0785.05014
Knuth, Donald E.
Two notes on notation. (English)
[J] Am. Math. Mon. 99, No.5, 403-422 (1992). ISSN 0002-9890

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.
[Ian Anderson (Glasgow)]

MSC 2000:: *05A99 Classical combinatorial problems

Keywords: notation; Stirling numbers

Citations: Zbl 0136.356

Cited in: Zbl 0818.05007

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]