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Topic: Number of lattice paths with given steps?
Replies: 7   Last Post: Nov 24, 2012 6:41 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Number of lattice paths with given steps?
Posted: Nov 21, 2012 9:26 PM
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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?

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