IV
Posts:
51
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.
|
|
