A lattice path from one point to another is 
-good if it lies completely below the
line
 |
(1) |
Hilton and Pederson (1991) show that the number of 
-good paths from (1, 
) to (
, 
)
under the condition 
is
 |
(2) |
where 
is a binomial
coefficient, and
 |
(3) |
where 
is the floor
function.
See also
Catalan Number, Lattice Path, Schröder Number
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References
Hilton, P. and Pederson, J. "Catalan Numbers, Their Generalization, and Their Uses." Math. Intel. 13, 64-75, 1991.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "p-Good Path." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/p-GoodPath.html