Counting tableaux with row and column bounds

It is well known that the generating function for tableaux of a given skew shape with r rows where the parts in the ith row are bounded by some nondecreasing upper and lower bounds which depend on i can be written in the form of a determinant of size r. We show that the generating function for tableaux of a given skew shape with r rows and c columns where the parts in the ith row are bounded by nondecreasing upper and lower bounds which depend …