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Concrete mathematics : a foundation for computer science

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n<br />

[ n-l 1<br />

n<br />

{I m<br />

Prestressed concrete<br />

<strong>mathematics</strong> is conn<br />

0 m<br />

n<br />

(i m >><br />

Crete <strong>mathematics</strong><br />

that’s preceded by (‘h...%)b<br />

a bewildering list<br />

of notations. K(al,. . . ,a,)<br />

F<br />

#A<br />

iz”l f(z)<br />

la..@1<br />

[m=nl<br />

[m\nl<br />

Im\nl<br />

[m-l-n1<br />

A NOTE ON NOTATION xi<br />

Stirling cycle number (the “first kind”) 245<br />

Stirling subset number (the “second kind”) 244<br />

Eulerian number 253<br />

Second-order Eulerian number 256<br />

radix notation <strong>for</strong> z,“=, akbk 11<br />

continuant polynomial 288<br />

hypergeometric function 205<br />

cardinality: number of elements in the set A 39<br />

coefficient of zn in f (2) 197<br />

closed interval: the set {x 1 016 x 6 (3} 73<br />

1 if m = n, otherwise 0 * 24<br />

1 if m divides n, otherwise 0 * 102<br />

1 if m exactly divides n, otherwise 0 * 146<br />

1 if m is relatively prime to n, otherwise 0 * 115<br />

*In general, if S is any statement that can be true or false, the bracketed<br />

notation [S] stands <strong>for</strong> 1 if S is true, 0 otherwise.<br />

Throughout this text, we use single-quote marks (‘. . . ‘) to delimit text as<br />

it is written, double-quote marks (“. . “) <strong>for</strong> a phrase as it is spoken. Thus,<br />

Also ‘nonstring’ is the string of letters ‘string’ is sometimes called a “string!’<br />

a string. An expression of the <strong>for</strong>m ‘a/be’ means the same as ‘a/(bc)‘. Moreover,<br />

logx/logy = (logx)/(logy) and 2n! = 2(n!).

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