A generalization of Ryserʹs theorem on term rank

In his work on classes of (0, 1)-matrices with given row and column sum vectors, Herbert Ryser proved that the maximum term rank possible in a normalized class, ρ, can be realized by a matrix having ρ (independent) 1ʹs in positions (1, ρ), (2, ρ − 1), … , (ρ, 1). We study the positions occupied by sets of t ⩽ ρ independent 1ʹs.