A 
-good path, for integer 
, is a lattice
path consisting of unit steps north and east such that every point of the path
lies strictly below the line
 |
(1)
|
Hilton and Pedersen (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.
