n Latin Rectangle [LR] based on
n is a 2-dimensional array of
r rows and
n columns, where
n, such that each entry is one of the integers
n and each of these integers occurs at most once in each row and at most once in each column.
Is it true that every
n LR can be extended to an
n LR (a Latin square [LS])? Why or why not?
Okay so my way of checking this is to first see what conditions need to be met that would make a LR unable to conform to a LS.
I will be making an assumption that the only case we need to worry about is the case where
r = n-1 because that is the most confined example. And to convert every other example where
r < n-1 to a LS is just a series of steps more trivial than the final step of the