#OK to post homework
#Victoria Chayes, 2/28/21, Assignment 11

Help:=proc(): print(`RandPnk(n,k), and RandPn(n), EstStatAnalOfLargestPart(n,K,N)`): end:
with(combinat):


#1 Using the same type as recursion as in Pnk(n,k) and Pn(n), and using the Wilf methodolgy (using pnk(n,k), write procedures RandPnk(n,k), and RandPn(n) that, respectively, genearte, unoformly at random, a partion of n with largest part k, and a partion of n.

RandPnk:=proc(n,k) local k1,L,L1:
if not (type(n,integer) and type(k,integer) and n>=1 and k>=1 )then
 RETURN([]):
fi:
if k>n then
 RETURN([]):
fi:
if k=n then
 RETURN([n]):
fi:
k1:=LD([seq(pnk(n-k,i),i=1..min(n-k,k))]):
[k,op(RandPnk(n-k,k1))]:
end:

RandPn:=proc(n) local k:
k:=LD([seq(pnk(n,i),i=1..n)]):
RandPnk(n,k):
end:



###########################
### Programs From Class ###
###########################

pnk:=proc(n,k) local k1:
option remember:
if not (type(n,integer) and type(k,integer) and n>=1 and k>=1 )then
 RETURN(0):
fi:
if n=k then
 RETURN(1):
else
 RETURN(add(pnk(n-k,k1),k1=1..min(k,n-k))):
fi:
end: