"William Elliot" wrote in news:Pine.NEB.email@example.com...
>> I'm looking for a formula for calculating the number of lattice paths in >> a >> rectangular quadratic integer lattice with given kind of steps and given >> numbers of steps of each kind. > > What's a rectangular quadratic integer lattice? Z^2 with no lattice order.
> I suppose are there four kinds of steps, up, down, left, right > and if some steps are missing, tough. In general, there could also steps (1,1) or (1,y) with different y be allowed.
> Now what the heck is a lattice path? Any finite path. > Any finite path from a point? > Any finite path from a point to another given point? The usual definition of a lattice path: the different kinds of lattice paths: the lattice paths you want.
Please concentrate your mind on this: I assume, the problem of given numbers of steps of each kind is a new quality of lattice path problems. Has someone experiences, literature references or ideas for this kind of problems?
>> That means all lattice paths with n1 steps (1,1), n2 steps (1,2), n3 >> steps (1,3) and so on - the numbers n1, n2, n3, ... are given. > What constitutes the step (1,2)? An 1-step in the one direction and a 2-step in the rectangular direction.
Please excuse me. I'm not a mathematician. I used only the notation like the articles and books which treat lattice paths. I thought the notation is known or plausible.