Interleavings of two translate to words reperesemting simple curves on a punctured torus. I think each one is also valid when extended in this case. The lex-min cyclic permutations are associated <--> their slope. Tjere are O(n^2) slopes admitting O(n) cyclic permutations. -- is there a good logical analysis of the 3D simplification base = slope for interleavings of 3? You can think of in terms of the cynical subdivision, as seen from the origin. Bill Sent from my iPhone On Jul 23, 2010, at 8:35 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 7/23/10, Michael Kleber <michael.kleber@gmail.com> wrote:
On Fri, Jul 23, 2010 at 12:34 PM, Fred lunnon <fred.lunnon@gmail.com> wrote: ... I'm satisfied with the first 12 terms validating the correctness of the symmetry-aware version. Just made the change, and it reproduced those 12 terms in 67 seconds. During the time I spent composing this email, it's gotten up to n=16:
1, 3, 9, 27, 75, 189, 447, 951, 1911, 3621, 6513, 11103, 18267, 29013, 44691, 67251, 98547
Great stuff! (methodically unclenching teeth)
I'll let it run for a while and post here. Allan is welcome to own the OEIS entry :-).
Yes indeed.
Any ideas on functional recursions, explicit expressions, asymptotics?
Not I; see "didn't have time to think" above...
Hmm ... evalf(log(98547/67251)/log(16/15)); 5.920521497 evalf(log(67251/44691)/log(15/14)); 5.923217032 I wonder if perchance f_3(n) = O(n^6) ??
f_2(n) = O(n^3) must follow straightforwardly via standard results from the explicit formula in A005598; but I presently haven't a clue why that should hold either.
Fred Lunnon
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun