REACH hours log
2/4 attended REACH meeting, wrote up minutes for the meeting (3 hrs.)
2/6 attended REACH meeting (2 hrs.).

This week: 5 Total: 5

2/11 attended REACH meeting (2 hrs.)
2/13 attended REACH meeting (2 hrs.)

This week: 4 Total: 9

2/18 attended REACH meeting (2 hrs.)
2/20 attended REACH meeting (2 hrs.)

This week: 4 Total: 13

2/25 attended REACH meeting (2 hrs.)
2/27 prepared a talk on Rui's and my work on Markov numbers, attended REACH meeting (3 hrs.)

This week: 5 Total: 18

3/4 attended REACH meeting (2 hrs.)
3/6 attended REACH meeting, took another stab at a markov-like recurrence in 4-variables. Alas,
      more head banging. (2 hrs.)

This week: 4 Total: 22

3/11 attended REACH meeting - looked at similar recurrences to the Markov numbers. (2 hrs.)
3/13 attended REACH meeting - looked at a similar recurrence. From initial tests on maple, it appears
       that the new recurrence we're looking has cancellations in the numerator via comparison to the markov
       numbers. Furthermore, we also get that the number of terms is also different, so if we have some sort of 
       combinatorial counting, entire monomials could be getting cancelled out. The denominators are the same
       when applying the u,v, or w operators on a triple whether with the markov recurrence or the new one. (2 hrs.)

This week: 4 Total: 26

3/18 attended REACH meeting (2 hrs.)
3/20 attended REACH meeting - Discussed with Gabriel and Ian the connection between the ptolemy 
        recurrence and markov numbers. (1.5 hrs)

This week: 4 Total: 29.5

3/23 Went through Gabe's e-mail relating perfect matchings of graphs to triangulations of polygons. Looked
       at markov snake graphs in terms of continued fraction numerators. (2 hrs.)

This week: 2 Total: 31.5

4/1 attended REACH meeting, worked with Ian; able to show denominators of the polynomials in a given branch 
      of the Markov polynomials are distinct. Looked at Markov numbers plotted as (a,b) with relatively prime coordinates.
      Alas, a conjecture about their ordering did not work out. (2 hrs.)
4/3 attended REACH meeting, we managed to show prove some inequalities in the plot of the Markov numbers on
      points with relatively prime coefficients. This puts asymptotics on the Dana-Scott recurrence terms, though
      this may have already been known. (2 hrs.)

This week: 4 Total: 35.5

4/8 attended REACH meeting, showed that numerators of Markov polynomials are distinct. (2 hrs.)
4/10 attended REACH meeting, started writing up work. (4 hrs.)

This week: 6 Total: 41.5

4/11/03 Writing up stuff. (2 hrs.)
4/12/03 More writing up stuff. (2 hrs.)

This week: 4 Total: 45.5

4/15/03 REACH meeting. 
4/17/03 REACH meeting.

This week: 4 Total: 49.5

4/22/03 Reach Meeting. More writing up. See the website for a .dvi of what's done so far. (5.5 hours)

This week: 5.5 Total: 55

4/25/03 REACH Meeting. Illustrating... (3 hrs).
4/27/03 Writing, REACH meeting. (5.5 hours).

This week: 8.5 Total: 63.5