#Homework by Mike Murr
#OK to post
#hw7

currentdir("/Users/michaelmurr/Documents/Mike/Experimental Math");

read `C7.txt`;

#counts(n): Displays the number of set-partitions of {1,…,n} into k
#parts, where k ranges from 1 to n

counts := proc(n) local k; 

seq(NuSPnk(n,k),k=1..n); 

end proc;

NuSPnk(2,1);
NuSPnk(2,2);
counts(2);
counts(3);
counts(4);
counts(5);

#ChooseK(n): Uses LD (Loaded Die) to choose a value for k

ChooseK :=proc(n) local k;

LD([seq(NuSPnk(n,k),k=1..n)]);

end proc;

ChooseK(5);
ChooseK(5);
ChooseK(5);

#RandSPn(n): Inputs a positive integer n and outputs a (uniformly)
# at random set partition of {1,…,n}

RandSPn := proc(n) local k, kk;

kk := ChooseK(n);

print(kk);

RandSPnk(n,kk);

end proc;

RandSPn(5);
RandSPn(5);