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.
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