SSL Minutes for Tuesday, Nov. 18, 2003
Notes: Sam Lachterman
Snacks: Martin Hock
Hal will take notes on Thursday.
Paul will bring snacks Thursday.
Jim: Have we found out about posting sequences to the Online Encyclopedia of
Integer Sequences?
Paul: Sam has done so--you fill out a form and then the moderator decides
what gets posted.
Jim: A while back we found that for the sequence of matchings of the
2-by-2-by-n (cube) snake, every other term is a perfect square (and the
ones which are not are twice a perfect square). Moreover, we showed that
the weighted "version" is also a perfect square (or twice a square) for some
natural weighting scheme of the edges. Has anyone looked into proving the
positivty of the coefficients? That is, that they are counting something?
(No).
Jim: Well let's move on, if you all have moved on. Has anyone looked at the
two articles which I sent in a prior e-mail about Markoff-like entities?
That is, entities whose integer solutions can be found from a fundamental
one? Entities of the form: ax^2+by^2+cz^2=dxyz for constants a,b,c,d
Can we find a geometrical picture?
[Jim goes to board]
Given a triple (a,b,c) such that a