More Quetian max/min permutation-type sequences?

[Edwin Clark]

Let f_n: [n]^n -> R, n = 1,2,... be any family of functions. 

(Here [n] = {1,2,...,n} and R = reals.)

Define amax_f(n) = maximum value of f_n(p(1),...,p(n)) where p runs thru 
all permutations of 1,2,...,n.

Define amin_f(n) = mimimum value of f_n(p(1),...,p(n)) where p runs thru 
all permutations of 1,2,...,n.

Now, lets run through all possible choices for the f_n's and see what 
sequences we get.:-) 

Edwin