2004-04-15 SSL Minutes

Note-taker: Hal
Snack-bringer:

Note-taker for next time: ??? (see below)
Snack-bringer for next time: Hal

Hal is taking notes.  I arrived early to ask Sam to explain
q-binomials to me.  He began by defining the q-analog to factorial,

    q-factorial(N) := (1)*(1+q)* ... *(1+q+...+q^(N-2))*(1+q+...+q^(N-1))

Then, q-binomials are defined as you would expect:

    qbin(n,k) := q-factorial(N) / ( q-factorial(k) * q-factorial(n-k))

Note that (1+q+q^2...+q^(n-1)) = (1-q^n)/(1-q). (as long as q!=1.)

    qbin(n,k) = product(1-q^i,i=k+1..n) / product(1-q^i,i=1..n-k)

## begin maple code ##
qbin := (n,k) -> product(1-q^i,i=k+1..n)/product(1-q^i,i=1..n-k);
## end maple code ##

Then the meeting more or less began.  Jim will "very likely" raise the
salary cap.  So prepare to prepare timesheets.

When is end of SSL?  May 15 or so. Do not want to interfere with exams
too much.  Feel free to finish up over the summer. Keep in touch.

Jim will come up with a date for the end-of-semester dinner some time.

We moved into the other room without thinking to assign duties for
Tuesday, but I assembled a table to help:

AUTHOR            BYTES
-------           -------------
Martin Hock       11026 + 12573 + 1517 + 3245 + 3871 + 9402        = 41634
Hal Canary        14378 + 2494  + 2532 + 4355 + 4897 + 5107 + 7408 = 41171
Carl Edquist      3505  + 3567  + 5810 + 6989 + 7925 + 8530        = 36326
Emilie Hogan      1615  + 2553  + 2933 + 7395 + 7841 + 8080        = 30417
Paul Heideman     11434 + 1289  + 2326 + 2811 + 3105 + 3795 + 5368 = 30128
Sam Lachterman    1615  + 3206  + 3404 + 3858 + 4079 + 5209 + 6906 = 28277
Brendan Younger   117   + 4027  + 5654                             =  9798
Abigail Scott     3888  + 4431                                     =  8319
Stephen Griffeth  3496  + 3866                                     =  7362

If we go by bytes, either Brendan or Sam should do notes on
Tuesday. If we go by number of meetings, it should be Martin, Carl,
Emilie, or Brendan.  Someone speak up.

I volunteer for snack on Tuesday.

I worked on the q-binomial thing.  it is NOT as simple as inserting
[n,k] for each (n,k), but there might be a nice formula.  I just don't
see it yet.

See file:/undergrad.math.wisc.edu/newton-with-a-vengance/
(i.e., log in to under.math.wisc.edu and look in the directory 
/home-uc/hal/newton-with-a-vengance/)

Emilie gave a partial proof of the conjectured relationship between 
certain quadratic recurrences and linear recurrences.  (She proved
the induction step, but not the base case.)  She promised an email.

Carl has been working on some TeX.

That's all I wrote down.  After the meeting I demoed xfig.  Then got into
argument about the countability of the cardinals with Sam.  Then I
proved to Carl that cross products aren't associative.