Asymptotic distribution of the number of rectangles arising in binomial trials

The simultaneous occurrence of independent and identical Binomial trials at n^2
locations of an n\times n lattice may randomly produce a specifi ed confi guration
comprising the same event. One con guration being a rectangle, this paper nds
factorial moments of the number of these rectangles. Asymptotic behavior of the
random variable de fined is also investigated.