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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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 IV Posts: 356 Registered: 9/1/11
Re: Number of lattice paths with given steps?
Posted: Nov 21, 2012 2:54 PM

"William Elliot" wrote in
news:Pine.NEB.4.64.1211201932210.3614@panix3.panix.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.

Date Subject Author
11/20/12 IV
11/20/12 William Elliot
11/21/12 IV
11/21/12 William Elliot
11/22/12 IV
11/22/12 William Elliot
11/24/12 IV
11/20/12 trj