MATH G6238: Enumerative Combinatorics
Spring 2002
This page is
www.math.columbia.edu/~bayer/S02/combinatorics
Section 001 (Bayer)
Tuesdays and Thursdays, 2:40pm-3:55pm
507 Mathematics Building
Dave Bayer (x42643, 426 Mathematics,
www.math.columbia.edu/~bayer)
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Directory of Classes :
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Text:
-
Enumerative Combinatorics, Volume I by Richard P. Stanley.
This text exists in three editions:
- Second printing, hardcover: Cambridge Studies in Advanced Mathematics 49, Cambridge University Press,
1997, ISBN 0521553091.
University bookstore or
AddALL ($40-$60).
- Second printing, paperback: Cambridge Studies in Advanced Mathematics 49, Cambridge University Press, 2000, ISBN 0521663512.
AddALL ($22-$30).
- First printing, hardcover: Wadsworth & Brooks/Cole, 1986, ISBN 0534065465.
These editions have nearly identical main texts; more recent
editions have some errors corrected in the main text, and
more errata and exercises appended at the end of the book.
Richard Stanley maintains a web site Information on
Enumerative Combinatorics where this is
explained better than I possibly can, and where the most
recent errata and exercises can be downloaded. Whichever
edition you obtain, you will end up transcribing some errata by hand
into the main text, so get your hands on any edition you can.
Course materials: Course materials will be posted in Acrobat PDF format. Your browser
can be trained to automatically open these files with Acrobat Reader, a free program which you can
download from http://www.adobe.com/products/acrobat/readermain.html.
This Mathematica file computes the rational generating function
of an integer sequence, when the sequence is (apparently) rational. As an example,
I confirm that the known data
(google:njas)
1, 1, 2, 5, 14, 50, 233, 1249, 7595, 49566, 339722, 2406841, 17490241,
129664753, 977526957, 7475907149, 57896349553, 453382272049,
3585853662949, 28615703421545
for triangulations of a 2-sphere
does not appear to be rational.
These PDF files are scans of my unedited, handwritten notes made in preparation for class. They are offered as-is, and are probably only useful
to people taking the course, as a supplement to the text and their own notes.
- notes.1.22.pdf
...Class notes, Tuesday, January 22
- notes.1.24.pdf
...Class notes, Thursday, January 24
- notes.1.29.pdf
...Class notes, Tuesday, January 29
- notes.1.31.pdf
...Class notes, Thursday, January 31
- notes.2.5.pdf
...Class notes, Tuesday, February 5
- notes.2.7.pdf
...Class notes, Thursday, February 7
- notes.2.12.pdf
...Class notes, Tuesday, February 12
- notes.2.14.pdf
...Class notes, Thursday, February 14
- notes.2.19.pdf
...Class notes, Tuesday, February 19
- notes.2.21.pdf
...Class notes, Thursday, February 21