tag:blogger.com,1999:blog-6555947.post4123751800944097598..comments2023-03-24T07:33:48.282-06:00Comments on The Geomblog: Generalized(?) Dyck PathsSuresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6555947.post-73570427003065918882007-04-07T00:45:00.000-06:002007-04-07T00:45:00.000-06:00Anon1: thanks for the tip - that's what we needed ...Anon1: thanks for the tip - that's what we needed !<BR/><BR/>Anon2: sounds fascinating. I don't know anything about it, but if you have a link I'd love to hear more.Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-55195362417354915222007-04-07T00:40:00.000-06:002007-04-07T00:40:00.000-06:00Hi I looked at an isomorphic catalan system all su...Hi <BR/><BR/>I looked at an isomorphic catalan system all summer and they are totally awesome. Sleator Tarjan and Thruston tightly bounded the rotation distance of binary trees for a fixed n using hyperbolic geometry--we were tying to produce examples of triangulations that exhibit the diameter. We came up with a bunch of stuff but not quite what we were looking for.<BR/><BR/>Do you know if anyone has looked Dyck paths as a type of path homotopy? Eg if you glue the lattice square to get the torus then a diagonal path wraps quotients into a loop. <BR/><BR/>-mAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-85967319024616069572007-04-03T13:28:00.000-06:002007-04-03T13:28:00.000-06:00See http://www.research.att.com/~njas/sequences/A0...See http://www.research.att.com/~njas/sequences/A009766<BR/><BR/>The formula you are looking for seems to be<BR/><BR/>a(n, k)= binomial(n+k,n)*(n-k+1)/(n+1)<BR/><BR/>In particular, a(n, n-1) = a(n, n), which is clear geometrically.Anonymousnoreply@blogger.com