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.