On Wed, 21 Nov 2012, IV wrote: > "William Elliot" wrote in > > > > 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.
Define the step (1,y) on the infinite grid Z^2.
> > 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.
The usual graph theory definition of a path p from a point a, to a point b, is a finite series of adjacent points starting with a and ending with b. Is that what you mean? Are you wanting to consider infinite paths? How about paths that don't cross themselves?
> 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? > Who's to know what your talking about when you don't define your terms?