Question on meaning of a symbol: long thin C

Question

I don't know how to write it in $\LaTeX.$ It is a tall skinny bold C. This is the context: A set is defined by: The formula

where $\complement\atop{\smash \scriptstyle i}$ is the thing I don't understand. The $i$ is actually directly underneath the weird $C$ in this case. Can anyone explain what this means?

Does it look like $$E_f = {i:{\complement_i} L(x)\ne 0}$$? (The $\complement$ is \complement.) — MJD, Jul 03 '12 at 14:41
Yes! But without the square brackets (not sure why I added those). — 098765, Jul 03 '12 at 14:43
Though it's kind of bolder and taller but that could just be the book. — 098765, Jul 03 '12 at 14:44
It might be easier for us, if you could add some information about the book you are reading. — Siminore, Jul 03 '12 at 14:50
It's Proposition 4.2.2 in Stanley's "Enumerative Combinatorics", I think this is a link to the page http://books.google.co.uk/books?id=EvJg1VjIGyMC&pg=PA204&source=gbs_toc_r&cad=4#v=onepage&q&f=false — 098765, Jul 03 '12 at 14:54
There's a page on notation at the beginning of that google books preview, but it's not mentioned there. Is there a page on notation that it misses out? — Ben Millwood, Jul 03 '12 at 15:01
On page 6 it seems that $\complement_i L(x)$ denotes the $i$-th coefficient of the formal power series $L(x)$. — martini, Jul 03 '12 at 15:06
(I deleted a comment earlier which referred to a now-deceased link) — Ben Millwood, Sep 27 '12 at 02:17

score 7 · Accepted Answer · answered Jul 03 '12 at 15:05

7

It's the coefficient operator. It extracts the ith coefficient of the Taylor expansion. This is used a lot in combinatorics with generating functions.

answered Jul 03 '12 at 15:05

ex0du5

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Thanks for this. I've just seen it explained on page 3 as well. – 098765 Jul 03 '12 at 15:07
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What about the notation $[z^n]f(z)$ to denote the coefficient? – Yai0Phah Jul 03 '12 at 15:14
@Frank Science : It may happen that a standard notation is not the best one, but the main property that's interesting of a standard notation is that it is 'standard', i.e. everyone uses it and everyone is used to it. Sometimes this is because everyone tends to like it after working for a while in the field where the notation is used. It doesn't mean your idea is good or wrong, just that if you want to make a new notation popular, usually you prove a few things in that field of research that makes the use of this new notation more useful than the previous one. – Patrick Da Silva Jul 03 '12 at 15:18
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@PatrickDaSilva It's not mine. I saw it in Don Knuth's books, for example, The Art of Computer Programming, or Concrete Mathematics. – Yai0Phah Jul 03 '12 at 15:19
@Frank Science : I didn't know. But still, my comment applies ; perhaps people working with generating functions prefer the $\complement$ notation to the $[z^n]f(z)$ notation. – Patrick Da Silva Jul 03 '12 at 18:12
They don't. In fact the second edition of Stanley (http://www-math.mit.edu/~rstan/ec/ec1/) uses the $[z^n] f(z)$ notation (see p. 11). – Michael Lugo Feb 08 '16 at 17:51

Question on meaning of a symbol: long thin C

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