
Re: This Week's Finds in Mathematical Physics (Week 236)
Posted:
Jul 30, 2006 12:01 PM


> Maybe you meant Motzkin *trees*.
No, I did mean paths:
"A001006 Motzkin numbers: number of ways of drawing any number of nonintersecting chords among n points on a circle.
Also number of Motzkin npaths: paths from (0,0) to (n,0) in an n X n grid using only steps U = (1,1), F = (1,0) and D = (1,1)."
http://www.research.att.com/~njas/sequences/A001006
But of course there are loads of combinatorial interpretations, including the trees you mention (which was actually the way I found the link between Leinster and Fiore's construction and the Motzkin numbers.)
> If anyone who knows categories, combinatorics and Galois theory > wants to become a math grad student at UCR and work on the project > Jeff and I dropped, they should contact me.
Now, that's an excellent offer.

