4 Nov
2005
4 Nov
'05
2:53 p.m.
Oops, I think I switched p and q. Should have said ... the probability that an nxn bitmatrix will have (mod 2) rank = k is 2 n - k + 1 k + 1 (n - k) (q ; q) (q ; q) q k n - k P(n,k) := -------------------------------------------, (q; q) n - k if the entries are 1 with probability p = 1-q . Thus the peculiar base q identity Sum P(n,k) = 1. k In particular, the probability of being nonsingular is just (q;q)_n. Sorry for the noise, --rwg