[math/9205211] Two notes on notation
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arXiv:math/9205211 (math)
[Submitted on 1 May 1992]
Title:Two notes on notation
Authors:Donald E. Knuth<br>View a PDF of the paper titled Two notes on notation, by Donald E. Knuth
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Abstract: The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "[P]" for the function which is 1 when the Boolean condition P is true and 0 otherwise. This notation can encourage and clarify the use of characteristic functions and Kronecker deltas in sums and integrals.
The second notation puts Stirling numbers on the same footing as binomial coefficients. Since binomial coefficients are written on two lines in parentheses and read "n choose k", Stirling numbers of the first kind should be written on two lines in brackets and read "n cycle k", while Stirling numbers of the second kind should be written in braces and read "n subset k". (I might say "n partition k".) The written form was first suggested by Imanuel Marx. The virtues of this notation are that Stirling partition numbers frequently appear in combinatorics, and that it more clearly presents functional relations similar to those satisfied by binomial coefficients.
Comments:<br>Abstract added by Greg Kuperberg
Subjects:
History and Overview (math.HO)
Report number:<br>Knuth migration 11/2004
Cite as:<br>arXiv:math/9205211 [math.HO]
(or<br>arXiv:math/9205211v1 [math.HO] for this version)
https://doi.org/10.48550/arXiv.math/9205211
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arXiv-issued DOI via DataCite
Journal reference:<br>Amer. Math. Monthly 99 (1992), no. 5, 403--422
Submission history<br>From: Maggie McLoughlin [view email]<br>[v1]<br>Fri, 1 May 1992 00:00:00 UTC (25 KB)
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