Abstract
A μ-way latin trade of volume s is a set of μ partial latin rectangles (of inconsequential size) containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial latin rectangles, and such that row i in each of the μ partial latin rectangles contains, set-wise, the same symbols and column j, likewise. In this paper we show that all μ-way latin trades with sufficiently large volumes exist, and state some theorems on the non-existence of μ-way latin trades of certain volumes. We also find the set of possible volumes (that is, the volume spectrum) of μ-way latin trades for μ = 4 and 5. (The case μ = 2 was dealt with by Fu, and the case μ = 3 by the present authors.)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have