A Full Description of Polytopes Related to the Index of the Lowest Nonzero Row of an Assignment Matrix

where Mk,n is the set of all k-by-n matrices with coefficients in {0, 1} and the variables y l are interpreted as follows: y i l = 1 if and only if z i = l. The matrix (y j) can be seen as a {0, 1} assignment matrix where each column contains exactly one coefficient equal to 1 while h denotes the index of the lowest row that is not identically equal to the zero row (cf. Fig. 1). Another variant of P is obtained by considering the index of the highest row that is not identically equal to the zero row. In this case we get the polytope