#OK to post
#Homework 19, Rebecca Embar

read `C18.txt`:
read `C19.txt`:

#1
#(i)
UmbT := proc(P,var,N) local n:
	[seq(Umb(P^n,var),n=1..N)]:
end:

#(ii) 
#(a) A000984
#	 Central binomial coefficients: binomial(2*n,n)
#(b) A002893
#	 Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k)
#(c) Not in OEIS
#(d) Not in OEIS
#(e) Not in OEIS

#2
#IsCond3G has as condition that 3->1 if 1 does not beat 3. 
#Thus, 1->2->3->1 is considered true when 1 and 3 are tied.
#In my opinion this is incorrect, and disagrees with the 
#generating function for the Condorcet scenario.

#Specifically, IsCond3G([2,0,0,1,1],[[0,1,1],[0,0,1]]) outputs
#true, while the generating function has 0 as coefficient for t^4.
#This can be fixed by using G:=[[0,1,0],[0,0,1]] rather than
#G:=[[0,1,1],[0,0,1]].

#Notably, this only seems to be an issue when v is even. Cond3G
#and the generating function (t^2-t+1)*t^3/((t-1)^6*(t+1)^5) agree 
#when v is odd.

#When G := [[0,1,0],[0,0,1]] is used, the entries in
#[seq(NuC(v,G),v=1..10] are half of the entries in Zs(10)
#This is because Zs(10) is doubling each entry to account 
#for both possibilities 1->2->3->1 and 1->3->2->1, and NuC(v,G) 
#is not doubling.