Talk:Meanders

What to think of the following correspondence?

Here is an example of a meander on a 5-by-3 grid:

A meander on a (5,3)-grid

IDs	Image
S, H, W, E, W, V, S, A, N, V, E, W, E, H, N, (2 orientations)

and the corresponding lattice graph (where a blue edge corresponds to an edge crossed by a meander) (unfortunately the correspondence is not one-to-one, since from the lattice graph we cannot determine which of the two possible choices applies for the central tile of the non self-crossing meander)

⦁	⎪	⦁	⎪	⦁	⎪	⦁
⎪		⎪		⎪		⎪
⦁	⎪	⦁	⎪	⦁	⎪	⦁
⎪		⎪		⎪		⎪
⦁	⎪	⦁	⎪	⦁	⎪	⦁
⎪		⎪		⎪		⎪
⦁	⎪	⦁	⎪	⦁	⎪	⦁
⎪		⎪		⎪		⎪
⦁	⎪	⦁	⎪	⦁	⎪	⦁
⎪		⎪		⎪		⎪
⦁	⎪	⦁	⎪	⦁	⎪	⦁

A kludge to get a one-to-one correspondence would be to add a diagonal edge (bottom left to top right) in the center, with the proviso that a meander cannot cross it.

— Daniel Forgues 07:51, 2 January 2012 (UTC)