Bill T. wrote: << 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.
That seems a little jaundiced to me. But I was naively thinking of the torus also, perhaps in a different way: Given three real numbers a,b,c > 0, linear independent of each other and arbitrary reals a_0, ab_0, c_0, consider the line in R^3 [thought of as tiled by unit cubes] F(t) = (at + a_0, bt + b_0, ct + c_0)) Then F(t) enters successive unit cubes via faces perpendicular to the x_1, x_2, or x_3 axis in a specific order, which yields a sequence of 1's, 2's and 3's. Then: Which sequences of 1's, 2's, 3's are possible from any ordered triple of a,b,c as above? Or in general, which sequences of 1's through n's are possible ? (Or is this equivalent to the original question?) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele