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A path composed of connected horizontal and vertical line segments, each passing between adjacent Lattice
Points. A lattice path is therefore a Sequence of points ,
, ...,
with
such that each
is a Lattice Point and
is obtained by offsetting one unit east (or west) or one unit
north (or south).
The number of paths of length from the Origin (0,0) to a point
which are restricted to east and north
steps is given by the Binomial Coefficient
.
See also Ballot Problem, Golygon, Kings Problem, Lattice Point, p-Good Path, Random Walk
References
Dickau, R. M. ``Shortest-Path Diagrams.''
http://forum.swarthmore.edu/advanced/robertd/manhattan.html.
Hilton, P. and Pederson, J. ``Catalan Numbers, Their Generalization, and Their Uses.'' Math. Intel. 13, 64-75, 1991.