  This article could be called "theme and variations" on Cantor's celebrated
diagonal argument. Given a square nxn tableau T=(a_i^j) on a finite alphabet A,
let L be the set of its row-words. The permanent Perm(T) is the set of words
a_{\pi(1)}^1 a_{\pi(2)}^2 ...a_{\pi(n)}^n, where \pi runs through the set of
permutations of n elements. Cantorian tableaux are those for which Perm(T)\cap
L=\emptyset. Let s=s(n) be the cardinality of A. We show in particular that for
large n, if s(n) <(1-\epsilon) n/log n then most of the tableaux are
non-Cantorian, whereas if s(n) >(1+\epsilon) n/log n then most of the tableaux
are Cantorian. We conclude our article by the study of infinite tableaux.
Consider for example the infinite tableaux whose rows are the binary expansions
of the real algebraic numbers in the unit interval. We show that the permanent
of this tableau contains exactly the set of binary expansions of all the
transcendental numbers in the unit interval.
