#please do not post homework
Kenneth Chan
Math 454
HW 15

1. 
RoG:=proc(k,n) local V,E,i,j,T1,v,Neighs,Moves,m,pt:

V:=[seq(seq(seq([i,j],j=1..n),i=1..k))]:

for i from 1 to nops(V) do
T1[V[i]]:=i:
od:

E:=[]:

for i from 1 to nops(V) do
 pt:=V[i]:

Moves:={[1..n,0],[0,1..n]}:
A rook can either move left and right or up and down
Neighs:={seq(pt+m,m in Moves)}:

#But many of them fall off the board, 
Neighs:=Neighs intersect convert(V,set):

#We append to the "list of neighbors" the set of neighbors of the current vertex BUT in terms of their "ids" (given by T1)
#getting a description of the graph in "cannical form"
E:=[op(E),{seq(T1[v],v in Neighs)}]:
od:


#We return the graph in "canonical form" where the vertices (members of V), are labelled by positive inetegers from 1 to nops(V)
#together with the "dictionary"
E,V:
SAW:=SAWnu(RoG(k,n)):
end:

2.NuGW([40,40],{[1,0],[0,1],[1,1],[2,2]})
any step with [1,0] or [0,1] will go above x=y

SeqGW([20,20,20],{[1,0,0],[0,1,0],[0,0,1],[1,1,1,]}